Continuous point symmetries in group field theories
NASA Astrophysics Data System (ADS)
Kegeles, Alexander; Oriti, Daniele
2017-03-01
We discuss the notion of symmetries in non-local field theories characterized by integro-differential equations of motion, from a geometric perspective. We then focus on group field theory (GFT) models of quantum gravity and provide a general analysis of their continuous point symmetry transformations, including the generalized conservation laws following from them.
Conformal field theory on affine Lie groups
Clubok, Kenneth Sherman
1996-04-01
Working directly on affine Lie groups, we construct several new formulations of the WZW model, the gauged WZW model, and the generic affine-Virasoro action. In one formulation each of these conformal field theories (CFTs) is expressed as a one-dimensional mechanical system whose variables are coordinates on the affine Lie group. When written in terms of the affine group element, this formulation exhibits a two-dimensional WZW term. In another formulation each CFT is written as a two-dimensional field theory, with a three- dimensional WZW term, whose fields are coordinates on the affine group. On the basis of these equivalent formulations, we develop a translation dictionary in which the new formulations on the affine Lie group are understood as mode formulations of the conventional formulations on the Lie group. Using this dictionary, we also express each CFT as a three-dimensional field theory on the Lie group with a four-dimensional WZW term. 36 refs.
Working Group Report: Lattice Field Theory
Blum, T.; et al.,
2013-10-22
This is the report of the Computing Frontier working group on Lattice Field Theory prepared for the proceedings of the 2013 Community Summer Study ("Snowmass"). We present the future computing needs and plans of the U.S. lattice gauge theory community and argue that continued support of the U.S. (and worldwide) lattice-QCD effort is essential to fully capitalize on the enormous investment in the high-energy physics experimental program. We first summarize the dramatic progress of numerical lattice-QCD simulations in the past decade, with some emphasis on calculations carried out under the auspices of the U.S. Lattice-QCD Collaboration, and describe a broad program of lattice-QCD calculations that will be relevant for future experiments at the intensity and energy frontiers. We then present details of the computational hardware and software resources needed to undertake these calculations.
Homogeneous cosmologies as group field theory condensates
NASA Astrophysics Data System (ADS)
Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo
2014-06-01
We give a general procedure, in the group field theory (GFT) formalism for quantum gravity, for constructing states that describe macroscopic, spatially homogeneous universes. These states are close to coherent (condensate) states used in the description of Bose-Einstein condensates. The condition on such states to be (approximate) solutions to the quantum equations of motion of GFT is used to extract an effective dynamics for homogeneous cosmologies directly from the underlying quantum theory. The resulting description in general gives nonlinear and nonlocal equations for the `condensate wavefunction' which are analogous to the Gross-Pitaevskii equation in Bose-Einstein condensates. We show the general form of the effective equations for current quantum gravity models, as well as some concrete examples. We identify conditions under which the dynamics becomes linear, admitting an interpretation as a quantum-cosmological Wheeler-DeWitt equation, and give its semiclassical (WKB) approximation in the case of a kinetic term that includes a Laplace-Beltrami operator. For isotropic states, this approximation reproduces the classical Friedmann equation in vacuum with positive spatial curvature. We show how the formalism can be consistently extended from Riemannian signature to Lorentzian signature models, and discuss the addition of matter fields, obtaining the correct coupling of a massless scalar in the Friedmann equation from the most natural extension of the GFT action. We also outline the procedure for extending our condensate states to include cosmological perturbations. Our results form the basis of a general programme for extracting effective cosmological dynamics directly from a microscopic non-perturbative theory of quantum gravity.
Quantum group symmetry of N=1 superconformal field theories
NASA Astrophysics Data System (ADS)
Jiménez, F.
1990-12-01
We use the Gómez-Sierra contour deformation techniques to show that N=1 superconformal field theories with {2c}/{3<1}, in their Coulomb gas version, contain a quantum group structure as an underlying symmetry. In particular, we construct from the thermal subalgebras of these theories, the representation spaces of the quantized universal enveloping superalgebra U q osp(2, 1) and show how to compute its R-matrix, the comultiplication rules and its quantum Clebsch-Gordan coefficients by using a convenient definition of the screened vertex operators and an explicit realization of its generators.
Mean field theory for U(n) dynamical groups
NASA Astrophysics Data System (ADS)
Rosensteel, G.
2011-04-01
Algebraic mean field theory (AMFT) is a many-body physics modeling tool which firstly, is a generalization of Hartree-Fock mean field theory, and secondly, an application of the orbit method from Lie representation theory. The AMFT ansatz is that the physical system enjoys a dynamical group, which may be either a strong or a weak dynamical Lie group G. When G is a strong dynamical group, the quantum states are, by definition, vectors in one irreducible unitary representation (irrep) space, and AMFT is equivalent to the Kirillov orbit method for deducing properties of a representation from a direct geometrical analysis of the associated integral co-adjoint orbit. AMFT can be the only tractable method for analyzing some complex many-body systems when the dimension of the irrep space of the strong dynamical group is very large or infinite. When G is a weak dynamical group, the quantum states are not vectors in one irrep space, but AMFT applies if the densities of the states lie on one non-integral co-adjoint orbit. The computational simplicity of AMFT is the same for both strong and weak dynamical groups. This paper formulates AMFT explicitly for unitary Lie algebras, and applies the general method to the Lipkin-Meshkov-Glick {\\mathfrak s}{\\mathfrak u} (2) model and the Elliott {\\mathfrak s}{\\mathfrak u} (3) model. When the energy in the {\\mathfrak s}{\\mathfrak u} (3) theory is a rotational scalar function, Marsden-Weinstein reduction simplifies AMFT dynamics to a two-dimensional phase space.
Cosmology from group field theory formalism for quantum gravity.
Gielen, Steffen; Oriti, Daniele; Sindoni, Lorenzo
2013-07-19
We identify a class of condensate states in the group field theory (GFT) formulation of quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from the fundamental quantum GFT dynamics, following the procedure used in ordinary quantum fluids. The effective dynamics is a nonlinear and nonlocal extension of quantum cosmology. We also show that any GFT model with a kinetic term of Laplacian type gives rise, in a semiclassical (WKB) approximation and in the isotropic case, to a modified Friedmann equation. This is the first concrete, general procedure for extracting an effective cosmological dynamics directly from a fundamental theory of quantum geometry.
Renormalizable Models in Rank Tensorial Group Field Theory
NASA Astrophysics Data System (ADS)
Geloun, Joseph Ben
2014-11-01
Classes of renormalizable models in the Tensorial Group Field Theory framework are investigated. The rank d tensor fields are defined over d copies of a group manifold or with no symmetry and no gauge invariance assumed on the fields. In particular, we explore the space of renormalizable models endowed with a kinetic term corresponding to a sum of momenta of the form . This study is tailored for models equipped with Laplacian dynamics on G D (case a = 1) but also for more exotic nonlocal models in quantum topology (case 0 < a < 1). A generic model can be written , where k is the maximal valence of its interactions. Using a multi-scale analysis for the generic situation, we identify several classes of renormalizable actions, including matrix model actions. In this specific instance, we find a tower of renormalizable matrix models parametrized by . In a second part of this work, we study the UV behavior of the models up to maximal valence of interaction k = 6. All rank tensor models proved renormalizable are asymptotically free in the UV. All matrix models with k = 4 have a vanishing β-function at one-loop and, very likely, reproduce the same feature of the Grosse-Wulkenhaar model (Commun Math Phys 256:305, 2005).
Flat connection, conformal field theory and quantum group
Kato, Mitsuhiro.
1989-07-01
General framework of linear first order differential equation for four-point conformal block is studied by using flat connection. Integrability and SL{sub 2} invariance restrict possible form of flat connection. Under a special ansatz classical Yang-Baxter equation appears as an integrability condition and the WZW model turns to be unique conformal field theory in that case. Monodromy property of conformal block can be easily determined by the flat connection. 11 refs.
Temesvári, T; De Dominicis, C
2002-08-26
We use the generic replica symmetric cubic field theory to study the transition of short-range Ising spin glasses in a magnetic field around the upper critical dimension. A novel fixed point is found from the application of the renormalization group. In the spin-glass limit, this fixed point governs the critical behavior of a class of systems characterized by a single cubic parameter. For this universality class, the spin-glass susceptibility diverges at criticality, whereas the longitudinal mode remains massive. The third mode, however, behaves unusually. The physical consequences of this unusual behavior are discussed, and a comparison with the conventional de Almeida-Thouless scenario is presented.
NASA Astrophysics Data System (ADS)
Lahoche, Vincent; Ousmane Samary, Dine
2017-02-01
This paper is focused on the functional renormalization group applied to the T56 tensor model on the Abelian group U (1 ) with closure constraint. For the first time, we derive the flow equations for the couplings and mass parameters in a suitable truncation around the marginal interactions with respect to the perturbative power counting. For the second time, we study the behavior around the Gaussian fixed point, and show that the theory is nonasymptotically free. Finally, we discuss the UV completion of the theory. We show the existence of several nontrivial fixed points, study the behavior of the renormalization group flow around them, and point out evidence in favor of an asymptotically safe theory.
Renormalization group equations and matching in a general quantum field theory with kinetic mixing
NASA Astrophysics Data System (ADS)
Fonseca, Renato M.; Malinský, Michal; Staub, Florian
2013-11-01
We work out a set of simple rules for adopting the two-loop renormalization group equations of a generic gauge field theory given in the seminal works of Machacek and Vaughn to the most general case with an arbitrary number of Abelian gauge factors and comment on the extra subtleties possibly encountered upon matching a set of effective gauge theories in such a framework.
a Natural Extension of the Conformal Lorentz Group in a Field Theory Context
NASA Astrophysics Data System (ADS)
László, András
In this paper a finite dimensional unital associative algebra is presented, and its group of algebra automorphisms is detailed. The studied algebra can physically be understood as the creation operator algebra in a formal quantum field theory at fixed momentum for a spin 1/2 particle along with its antiparticle. It is shown that the essential part of the corresponding automorphism group can naturally be related to the conformal Lorentz group. In addition, the nonsemisimple part of the automorphism group can be understood as "dressing" of the pure one-particle states. The studied mathematical structure may help in constructing quantum field theories in a non-perturbative manner. In addition, it provides a simple example of circumventing Coleman-Mandula theorem using non-semisimple groups, without SUSY.
Crystal Field Theory and the Angular Overlap Model Applied to Hydrides of Main Group Elements.
ERIC Educational Resources Information Center
Moore, E. A.
1990-01-01
Described is how crystal field theory and the angular overlap model can be applied to very simple molecules which can then be used to introduce such concepts as bonding orbitals, MO diagrams, and Walsh diagrams. The main-group compounds are used as examples and a switch to the transition metal complexes. (KR)
Group field theory as the second quantization of loop quantum gravity
NASA Astrophysics Data System (ADS)
Oriti, Daniele
2016-04-01
We construct a second quantized reformulation of canonical loop quantum gravity (LQG) at both kinematical and dynamical level, in terms of a Fock space of spin networks, and show in full generality that it leads directly to the group field theory (GFT) formalism. In particular, we show the correspondence between canonical LQG dynamics and GFT dynamics leading to a specific GFT model from any definition of quantum canonical dynamics of spin networks. We exemplify the correspondence of dynamics in the specific example of 3d quantum gravity. The correspondence between canonical LQG and covariant spin foam models is obtained via the GFT definition of the latter.
Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions
NASA Astrophysics Data System (ADS)
Carrozza, Sylvain; Oriti, Daniele; Rivasseau, Vincent
2014-04-01
We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for applications to quantum gravity models. In the process, we define the appropriate generalization of some key QFT notions, including connectedness, locality and contraction of (high) subgraphs. We also define a new notion of Wick ordering, corresponding to the subtraction of (maximal) melonic tadpoles. We then consider the simplest examples of dynamical 4-dimensional TGFT with gauge invariance conditions for the Abelian U(1) case. We prove that they are super-renormalizable for any polynomial interaction.
Renormalization-group theory for the phase-field crystal equation
NASA Astrophysics Data System (ADS)
Athreya, Badrinarayan P.; Goldenfeld, Nigel; Dantzig, Jonathan A.
2006-07-01
We derive a set of rotationally covariant amplitude equations for use in multiscale simulation of the two-dimensional phase-field crystal model by a variety of renormalization-group (RG) methods. We show that the presence of a conservation law introduces an ambiguity in operator ordering in the RG procedure, which we show how to resolve. We compare our analysis with standard multiple-scale techniques, where identical results can be obtained with greater labor, by going to sixth order in perturbation theory, and by assuming the correct scaling of space and time.
Impact of nonlinear effective interactions on group field theory quantum gravity condensates
NASA Astrophysics Data System (ADS)
Pithis, Andreas G. A.; Sakellariadou, Mairi; Tomov, Petar
2016-09-01
We present the numerical analysis of effectively interacting group field theory models in the context of the group field theory quantum gravity condensate analog of the Gross-Pitaevskii equation for real Bose-Einstein condensates including combinatorially local interaction terms. Thus, we go beyond the usually considered construction for free models. More precisely, considering such interactions in a weak regime, we find solutions for which the expectation value of the number operator N is finite, as in the free case. When tuning the interaction to the strongly nonlinear regime, however, we obtain solutions for which N grows and eventually blows up, which is reminiscent of what one observes for real Bose-Einstein condensates, where a strong interaction regime can only be realized at high density. This behavior suggests the breakdown of the Bogoliubov ansatz for quantum gravity condensates and the need for non-Fock representations to describe the system when the condensate constituents are strongly correlated. Furthermore, we study the expectation values of certain geometric operators imported from loop quantum gravity in the free and interacting cases. In particular, computing solutions around the nontrivial minima of the interaction potentials, one finds, already in the weakly interacting case, a nonvanishing condensate population for which the spectra are dominated by the lowest nontrivial configuration of the quantum geometry. This result indicates that the condensate may indeed consist of many smallest building blocks giving rise to an effectively continuous geometry, thus suggesting the interpretation of the condensate phase to correspond to a geometric phase.
Relational evolution of effectively interacting group field theory quantum gravity condensates
NASA Astrophysics Data System (ADS)
Pithis, Andreas G. A.; Sakellariadou, Mairi
2017-03-01
We study the impact of effective interactions onto relationally evolving group field theory (GFT) condensates based on real-valued fields. In a first step we show that a free condensate configuration in an isotropic restriction settles dynamically into a low-spin configuration of the quantum geometry. This goes hand in hand with the accelerated and exponential expansion of its volume, as well as the vanishing of its relative uncertainty which suggests the classicalization of the quantum geometry. The dynamics of the emergent space can then be given in terms of the classical Friedmann equations. In contrast to models based on complex-valued fields, solutions avoiding the singularity problem can only be found if the initial conditions are appropriately chosen. We then turn to the analysis of the influence of effective interactions on the dynamics by studying in particular the Thomas-Fermi regime. In this context, at the cost of fine-tuning, an epoch of inflationary expansion of quantum geometric origin can be implemented. Finally, and for the first time, we study anisotropic GFT condensate configurations and show that such systems tend to isotropize quickly as the value of the relational clock grows. This paves the way to a more systematic investigation of anisotropies in the context of GFT condensate cosmology.
Emergence of a low spin phase in group field theory condensates
NASA Astrophysics Data System (ADS)
Gielen, Steffen
2016-11-01
Recent results have shown how quantum cosmology models can be derived from the effective dynamics of condensate states in group field theory (GFT), where ‘cosmology is the hydrodynamics of quantum gravity’: the classical Friedmann dynamics for homogeneous, isotropic universes, as well as loop quantum cosmology (LQC) corrections to general relativity have been shown to emerge from fundamental quantum gravity. We take one further step towards strengthening the link with LQC and show, in a class of GFT models for gravity coupled to a free massless scalar field and for generic initial conditions, that GFT condensates dynamically reach a low spin phase of many quanta of geometry, in which all but an exponentially small number of quanta are characterised by a single spin j 0 (i.e. by a constant volume per quantum). As the low spin regime is reached, GFT condensates expand to exponentially large volumes, and the dynamics of the total volume follows precisely the classical Friedmann equations. This behaviour follows from a single requirement on the couplings in the GFT model under study. We present one particular simple case in which the dominant spin is the lowest one: {j}0=0 or, if this is excluded, {j}0=1/2. The type of quantum state usually assumed in the derivation of LQC is hence derived from the quantum dynamics of GFT. These results confirm and extend recent results by Oriti, Sindoni and Wilson-Ewing in the same setting.
Using a stochastic field theory to understand group behavior in microswimmer suspensions
NASA Astrophysics Data System (ADS)
Underhill, Patrick; Qian, Yuzhou; Kramer, Peter
2015-11-01
Active suspensions of microswimmers appear both in natural biological systems (e.g. bacteria or algae) and in synthetic systems. Even without external forcing they are out of equilibrium, which gives rise to interesting properties in both small and large concentrations of the particles. These properties have been observed in experiments as well as simulation/modeling approaches. It is important to understand how hydrodynamic interactions between active swimmers cause and/or alter the suspension properties including enhanced transport and mixing. One of the most successful approaches has been a mean field theory. However, in some situations the mean field theory makes predictions that differ significantly from experiments and direct (agent or particle based) simulations. There are also some quantities that cannot be calculated by the mean field theory. In this talk, we will describe our new approach which uses a stochastic field to overcome the limitations of the mean field assumption. It allows us to calculate how interactions between organisms alter the correlations and mixing in conditions where the mean field theory cannot.
Using a stochastic field theory to understand group behavior in microswimmer suspensions
NASA Astrophysics Data System (ADS)
Underhill, Patrick; Qian, Yuzhou; Kramer, Peter
Active suspensions of microswimmers appear both in natural biological systems (e.g. bacteria or algae) and in synthetic systems. Even without external forcing they are out of equilibrium, which gives rise to interesting properties in both small and large concentrations of the particles. These properties have been observed in experiments as well as simulation/modeling approaches. It is important to understand how hydrodynamic interactions between active swimmers cause and/or alter the suspension properties including enhanced transport and mixing. One of the most successful approaches has been a mean field theory. However, in some situations the mean field theory makes predictions that differ significantly from experiments and direct (agent or particle based) simulations. There are also some quantities that cannot be calculated by the mean field theory. In this talk, we will describe our new approach which uses a stochastic field to overcome the limitations of the mean field assumption. It allows us to calculate how interactions between organisms alter the correlations and mixing in conditions where the mean field theory cannot.
Quantum Field Theories with Symmetries in the Wilsonian Exact Renormalization Group
NASA Astrophysics Data System (ADS)
Vian, F.
1999-05-01
The purpose of the present thesis is the implementation of symmetries in the Wilsonian Exact Renormalization Group (ERG) approach. After recalling how the ERG can be introduced in a general theory (i.e. containing both bosons and fermions, scalars and vectors) and having applied it to the massless scalar theory as an example of how the method works, we discuss the formulation of the Quantum Action Principle (QAP) in the ERG and show that the Slavnov-Taylor identities can be directly derived for the cutoff effective action at any momentum scale. Firstly the QAP is exploited to analyse the breaking of dilatation invariance occurring in the scalar theory in this approach. Then we address SU(N) Yang-Mills theory and extensively treat the key issue of the boundary conditions of the flow equation which, in this case, have also to ensure restoration of symmetry for the physical theory. In case of a chiral gauge theory, we show how the chiral anomaly can be obtained in the ERG. Finally, we extend the ERG formulation to supersymmetric (gauge) theories. It is emphasized regularization is implemented in such a way that supersymmetry is preserved.
NASA Astrophysics Data System (ADS)
de Cesare, Marco; Sakellariadou, Mairi
2017-01-01
We study the expansion of the Universe using an effective Friedmann equation obtained from the dynamics of GFT (Group Field Theory) isotropic condensates. The evolution equations are classical, with quantum correction terms to the Friedmann equation given in the form of effective fluids coupled to the emergent classical background. The occurrence of a bounce, which resolves the initial spacetime singularity, is shown to be a general property of the model. A promising feature of this model is the occurrence of an era of accelerated expansion, without the need to introduce an inflaton field with an appropriately chosen potential. We discuss possible viability issues of this scenario as an alternative to inflation.
NASA Astrophysics Data System (ADS)
Banks, Tom
2008-09-01
1. Introduction; 2. Quantum theory of free scalar fields; 3. Interacting field theory; 4. Particles of spin one, and gauge invariance; 5. Spin 1/2 particles and Fermi statistics; 6. Massive quantum electrodynamics; 7. Symmetries, Ward identities and Nambu Goldstone bosons; 8. Non-abelian gauge theory; 9. Renormalization and effective field theory; 10. Instantons and solitons; 11. Concluding remarks; Appendices; References; Index.
NASA Astrophysics Data System (ADS)
Wang, Juven; Gu, Zheng-Cheng; Wen, Xiao-Gang
The challenge of identifying symmetry-protected topological states (SPTs) is due to their lack of symmetry-breaking order parameters and intrinsic topological orders. For this reason, it is impossible to formulate SPTs under Ginzburg-Landau theory or probe SPTs via fractionalized bulk excitations and topology-dependent ground state degeneracy. However, the partition functions from path integrals with various symmetry twists are universal SPT invariants, fully characterizing SPTs. In this work, we use gauge fields to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology. This allows us to express the SPT invariants in terms of continuum field theory. We show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravity actions describe the beyond-group-cohomology SPTs, recently observed by Kapustin. We find new examples of mixed gauge-gravity actions for U(1) SPTs in 3+1D and 4+1D via the Stiefel-Whitney class and the gravitational Chern-Simons term. [Work based on Phys. Rev. Lett. 114, 031601 (2015) arXiv:1405.7689
Kheirandish, F.; Amooshahi, M.
2008-11-18
Quantum field theory of a damped vibrating string as the simplest dissipative scalar field theory is investigated by introducing a minimal coupling method. The rate of energy flowing between the system and its environment is obtained.
Covariant Noncommutative Field Theory
Estrada-Jimenez, S.; Garcia-Compean, H.; Obregon, O.; Ramirez, C.
2008-07-02
The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced.
NASA Technical Reports Server (NTRS)
Holman, Gordon D.
1989-01-01
The primary purpose of the Theory and Modeling Group meeting was to identify scientists engaged or interested in theoretical work pertinent to the Max '91 program, and to encourage theorists to pursue modeling which is directly relevant to data which can be expected to result from the program. A list of participants and their institutions is presented. Two solar flare paradigms were discussed during the meeting -- the importance of magnetic reconnection in flares and the applicability of numerical simulation results to solar flare studies.
Group theories: relevance to group safety studies.
Benevento, A L
1998-01-01
Promoting safety in the workplace has been attempted in a variety of ways. Increasingly, industries are using groups such as safety teams and quality circles to promote worker safety. Group influences on individual behavior and attitudes have long been studied in the social psychology literature, but the theories have not been commonly found outside the psychology arena. This paper describes the group theories of group polarization, risky shift, social loafing, groupthink and team think and attempts to apply these theories to existing studies that examine work group influences on safety. Interesting parallels were found but only one study examined group influences as their primary focus of research. Since groups are increasingly used for safety promotion, future research on safety that studies group influences with respect to current group theories is recommended.
ERIC Educational Resources Information Center
Morpurgo, Simone
2007-01-01
The principles of symmetry and group theory are applied to the zero-order wavefunctions associated with the strong-field t[subscript 2g][superscript 2] configuration and their symmetry-adapted linear combinations (SALC) associated with the generated energy terms are derived. This approach will enable students to better understand the use of…
Naive Theories of Social Groups
ERIC Educational Resources Information Center
Rhodes, Marjorie
2012-01-01
Four studies examined children's (ages 3-10, Total N = 235) naive theories of social groups, in particular, their expectations about how group memberships constrain social interactions. After introduction to novel groups of people, preschoolers (ages 3-5) reliably expected agents from one group to harm members of the other group (rather than…
NASA Astrophysics Data System (ADS)
He, Huan; Zheng, Yunqin; von Keyserlingk, Curt
2017-01-01
Dijkgraaf-Witten (DW) theories are of recent interest to the condensed matter community, in part because they represent topological phases of matter, but also because they characterize the response theory of certain symmetry protected topological (SPT) phases. However, as yet there has not been a comprehensive treatment of the spectra of these models in the field theoretic setting even for Abelian gauge groups, the goal of this work is to fill the gap in the literature, especially for a selection of DW models with Abelian gauge groups but non-Abelian topological order. Particularly, we focus on the appearance of non-Abelian statistics in type-III twisted DW theories with Abelian gauge groups Z2⊗3. There are only 22 distinguishable line operators, and their fusion rules and correlation functions are calculated. The flux insertion operators have quantum dimension 2, which clearly demonstrates the non-Abelian topological order of type-III twisted DW theories.
Logarithmic conformal field theory
NASA Astrophysics Data System (ADS)
Gainutdinov, Azat; Ridout, David; Runkel, Ingo
2013-12-01
Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more
Remainder Wheels and Group Theory
ERIC Educational Resources Information Center
Brenton, Lawrence
2008-01-01
Why should prospective elementary and high school teachers study group theory in college? This paper examines applications of abstract algebra to the familiar algorithm for converting fractions to repeating decimals, revealing ideas of surprising substance beneath an innocent facade.
Beyond mean field theory: statistical field theory for neural networks
Buice, Michael A; Chow, Carson C
2014-01-01
Mean field theories have been a stalwart for studying the dynamics of networks of coupled neurons. They are convenient because they are relatively simple and possible to analyze. However, classical mean field theory neglects the effects of fluctuations and correlations due to single neuron effects. Here, we consider various possible approaches for going beyond mean field theory and incorporating correlation effects. Statistical field theory methods, in particular the Doi–Peliti–Janssen formalism, are particularly useful in this regard. PMID:25243014
Reverse engineering quantum field theory
NASA Astrophysics Data System (ADS)
Oeckl, Robert
2012-12-01
An approach to the foundations of quantum theory is advertised that proceeds by "reverse engineering" quantum field theory. As a concrete instance of this approach, the general boundary formulation of quantum theory is outlined.
Lectures on Matrix Field Theory
NASA Astrophysics Data System (ADS)
Ydri, Badis
The subject of matrix field theory involves matrix models, noncommutative geometry, fuzzy physics and noncommutative field theory and their interplay. In these lectures, a lot of emphasis is placed on the matrix formulation of noncommutative and fuzzy spaces, and on the non-perturbative treatment of the corresponding field theories. In particular, the phase structure of noncommutative $\\phi^4$ theory is treated in great detail, and an introduction to noncommutative gauge theory is given.
Computational quantum field theory
NASA Astrophysics Data System (ADS)
Grobe, Rainer
2006-05-01
I will give an overview on recent attempts to solve the time-dependent Dirac equation for the electron-positron field operator. These numerical solutions permit a first temporally and spatially resolved insight into the mechanisms of how an electron-positron pair can be created from vacuum in a very strong force field. This approach has helped to illuminate a wide range of controversial questions. Some of these questions arise for complicated physical situations such as how an electron scatters off a supercritical potential barrier (Klein paradox). This requires the application of quantum field theory to study the combined effect of the pair-production due to the supercriticality of the potential together with the scattering at the barrier involving the Pauli-principle. Other phenomena include Schr"odinger's Zitterbewegung and the localization problem for a relativistic particle. This work has been supported by the NSF and Research Corporation. P. Krekora, K. Cooley, Q. Su and R. Grobe, Phys. Rev. Lett. 95, 070403 (2005). P. Krekora, Q. Su and R. Grobe, Phys. Rev. Lett. 93, 043004 (2004). P. Krekora, Q. Su and R. Grobe, Phys. Rev. Lett. 92, 040406 (2004).
Groups in the radiative transfer theory
NASA Astrophysics Data System (ADS)
Nikoghossian, Arthur
2016-11-01
The paper presents a group-theoretical description of radiation transfer in inhomogeneous and multi-component atmospheres with the plane-parallel geometry. It summarizes and generalizes the results obtained recently by the author for some standard transfer problems of astrophysical interest with allowance of the angle and frequency distributions of the radiation field. We introduce the concept of composition groups for media with different optical and physical properties. Group representations are derived for two possible cases of illumination of a composite finite atmosphere. An algorithm for determining the reflectance and transmittance of inhomogeneous and multi-component atmospheres is described. The group theory is applied also to determining the field of radiation inside an inhomogeneous atmosphere. The concept of a group of optical depth translations is introduced. The developed theory is illustrated with the problem of radiation diffusion with partial frequency distribution assuming that the inhomogeneity is due to depth-variation of the scattering coefficient. It is shown that once reflectance and transmittance of a medium are determined, the internal field of radiation in the source-free atmosphere is found without solving any new equations. The transfer problems for a semi-infinite atmosphere and an atmosphere with internal sources of energy are discussed. The developed theory allows to derive summation laws for the mean number of scattering events underwent by the photons in the course of diffusion in the atmosphere.
Stadler, K M; Yin, Z P; von Delft, J; Kotliar, G; Weichselbaum, A
2015-09-25
We show that the numerical renormalization group is a viable multi-band impurity solver for dynamical mean-field theory (DMFT), offering unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund metal problem for a three-band model on a Bethe lattice at 1/3 filling. The ground state is a Fermi liquid. The one-particle spectral function undergoes a coherence-incoherence crossover with increasing temperature, with spectral weight being transferred from low to high energies. Further, it exhibits a strong particle-hole asymmetry. In the incoherent regime, the self-energy displays approximate power-law behavior for positive frequencies only. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales.
NASA Astrophysics Data System (ADS)
Stadler, K. M.; Yin, Z. P.; von Delft, J.; Kotliar, G.; Weichselbaum, A.
2015-09-01
We show that the numerical renormalization group is a viable multi-band impurity solver for dynamical mean-field theory (DMFT), offering unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund metal problem for a three-band model on a Bethe lattice at 1 /3 filling. The ground state is a Fermi liquid. The one-particle spectral function undergoes a coherence-incoherence crossover with increasing temperature, with spectral weight being transferred from low to high energies. Further, it exhibits a strong particle-hole asymmetry. In the incoherent regime, the self-energy displays approximate power-law behavior for positive frequencies only. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales.
NASA Astrophysics Data System (ADS)
Katanin, A. A.
2015-06-01
We consider formulations of the functional renormalization-group (fRG) flow for correlated electronic systems with the dynamical mean-field theory as a starting point. We classify the corresponding renormalization-group schemes into those neglecting one-particle irreducible six-point vertices (with respect to the local Green's functions) and neglecting one-particle reducible six-point vertices. The former class is represented by the recently introduced DMF2RG approach [31], but also by the scale-dependent generalization of the one-particle irreducible representation (with respect to local Green's functions, 1PI-LGF) of the generating functional [20]. The second class is represented by the fRG flow within the dual fermion approach [16, 32]. We compare formulations of the fRG approach in each of these cases and suggest their further application to study 2D systems within the Hubbard model.
Quantum field theory of fluids.
Gripaios, Ben; Sutherland, Dave
2015-02-20
The quantum theory of fields is largely based on studying perturbations around noninteracting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is "freer", in the sense that the noninteracting theory also contains an infinite collection of quantum-mechanical free particles, corresponding to vortex modes. By computing a variety of correlation functions at tree and loop level, we give evidence that a quantum perfect fluid can be consistently formulated as a low-energy, effective field theory. We speculate that the quantum behavior is radically different from both classical fluids and quantum fields.
Field theory and particle physics
Eboli, O.J.P.; Gomes, M.; Santoro, A.
1990-01-01
This book contains the proceedings of the topics covered during the fifth Jorge Andre Swieca Summer School. The first part of the book collects the material devoted to quantum field theory. There were four courses on methods in Field Theory; H. O. Girotti lectured on constrained dynamics, R. Jackiw on the Schrodinger representation in Field Theory, S.-Y. Pi on the application of this representation to quantum fields in a Robertson-Walker spacetime, and L. Vinet on Berry Connections. There were three courses on Conformal Field Theory: I. Todorov focused on the problem of construction and classification of conformal field theories. Lattice models, two-dimensional S matrices and conformal field theory were looked from the unifying perspective of the Yang-Baxter algebras in the lectures given by M. Karowski. Parasupersymmetric quantum mechanics was discussed in the lectures by L. Vinet. Besides those courses, there was an introduction to string field theory given by G. Horowitz. There were also three seminars: F. Schaposnik reported on recent applications of topological methods in field theory, P. Gerbert gave a seminar on three dimensional gravity and V. Kurak talked on two dimensional parafermionic models. The second part of this proceedings is devoted to phenomenology. There were three courses on Particle Physics: Dan Green lectured on collider physics, E. Predrazzi on strong interactions and G. Cohen-Tanoudji on the use of strings in strong interactions.
Algebraic orbifold conformal field theories
Xu, Feng
2000-01-01
The unitary rational orbifold conformal field theories in the algebraic quantum field theory and subfactor theory framework are formulated. Under general conditions, it is shown that the orbifold of a given unitary rational conformal field theory generates a unitary modular category. Many new unitary modular categories are obtained. It is also shown that the irreducible representations of orbifolds of rank one lattice vertex operator algebras give rise to unitary modular categories and determine the corresponding modular matrices, which has been conjectured for some time. PMID:11106383
Extending Sociocultural Theory to Group Creativity
ERIC Educational Resources Information Center
Sawyer, Keith
2012-01-01
Sociocultural theory focuses on group processes through time, and argues that group phenomena cannot be reduced to explanation in terms of the mental states or actions of the participating individuals. This makes sociocultural theory particularly useful in the analysis of group creativity and group learning, because both group creativity and group…
Invariants from classical field theory
Diaz, Rafael; Leal, Lorenzo
2008-06-15
We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. By applying our methods to several field theories such as Abelian BF, Chern-Simons, and two-dimensional Yang-Mills theory, we obtain, respectively, the linking number for embedded submanifolds in compact varieties, the Gauss' and the second Milnor's invariant for links in S{sup 3}, and invariants under area-preserving diffeomorphisms for configurations of immersed planar curves.
From exceptional field theory to heterotic double field theory via K3
NASA Astrophysics Data System (ADS)
Malek, Emanuel
2017-03-01
In this paper we show how to obtain heterotic double field theory from exceptional field theory by breaking half of the supersymmetry. We focus on the SL(5) exceptional field theory and show that when the extended space contains a generalised SU(2)-structure manifold one can define a reduction to obtain the heterotic SO(3 , n) double field theory. In this picture, the reduction on the SU(2)-structure breaks half of the supersymmetry of the exceptional field theory and the gauge group of the heterotic double field theory is given by the embedding tensor of the reduction used. Finally, we study the example of a consistent truncation of M-theory on K3 and recover the duality with the heterotic string on T 3. This suggests that the extended space can be made sense of even in the case of non-toroidal compactifications.
The Nonlinear Field Space Theory
NASA Astrophysics Data System (ADS)
Mielczarek, Jakub; Trześniewski, Tomasz
2016-08-01
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the "Principle of finiteness" of physical theories, which once motivated the Born-Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
Quantum Field Theory, Revised Edition
NASA Astrophysics Data System (ADS)
Mandl, F.; Shaw, G.
1994-01-01
Quantum Field Theory Revised Edition F. Mandl and G. Shaw, Department of Theoretical Physics, The Schuster Laboratory, The University, Manchester, UK When this book first appeared in 1984, only a handful of W± and Z° bosons had been observed and the experimental investigation of high energy electro-weak interactions was in its infancy. Nowadays, W± bosons and especially Z° bosons can be produced by the thousand and the study of their properties is a precise science. We have revised the text of the later chapters to incorporate these developments and discuss their implications. We have also taken this opportunity to update the references throughout and to make some improvements in the treatment of dimen-sional regularization. Finally, we have corrected some minor errors and are grateful to various people for pointing these out. This book is designed as a short and simple introduction to quantum field theory for students beginning research in theoretical and experimental physics. The three main objectives are to explain the basic physics and formalism of quantum field theory, to make the reader fully proficient in theory calculations using Feynman diagrams, and to introduce the reader to gauge theories, which play such a central role in elementary particle physics. The theory is applied to quantum electrodynamics (QED), where quantum field theory had its early triumphs, and to weak interactions where the standard electro-weak theory has had many impressive successes. The treatment is based on the canonical quantization method, because readers will be familiar with this, because it brings out lucidly the connection between invariance and conservation laws, and because it leads directly to the Feynman diagram techniques which are so important in many branches of physics. In order to help inexperienced research students grasp the meaning of the theory and learn to handle it confidently, the mathematical formalism is developed from first principles, its physical
NASA Astrophysics Data System (ADS)
Maxfield, Travis; Robbins, Daniel; Sethi, Savdeep
2016-11-01
Studying a quantum field theory involves a choice of space-time manifold and a choice of background for any global symmetries of the theory. We argue that many more choices are possible when specifying the background. In the context of branes in string theory, the additional data corresponds to a choice of supergravity tensor fluxes. We propose the existence of a landscape of field theory backgrounds, characterized by the space-time metric, global symmetry background and a choice of tensor fluxes. As evidence for this landscape, we study the supersymmetric six-dimensional (2, 0) theory compactified to two dimensions. Different choices of metric and flux give rise to distinct two-dimensional theories, which can preserve differing amounts of supersymmetry.
The Theory of Conceptual Fields
ERIC Educational Resources Information Center
Vergnaud, Gerard
2009-01-01
The theory of conceptual fields is a developmental theory. It has two aims: (1) to describe and analyse the progressive complexity, on a long- and medium-term basis, of the mathematical competences that students develop inside and outside school, and (2) to establish better connections between the operational form of knowledge, which consists in…
Double field theory inspired cosmology
Wu, Houwen; Yang, Haitang E-mail: hyanga@scu.edu.cn
2014-07-01
Double field theory proposes a generalized spacetime action possessing manifest T-duality on the level of component fields. We calculate the cosmological solutions of double field theory with vanishing Kalb-Ramond field. It turns out that double field theory provides a more consistent way to construct cosmological solutions than the standard string cosmology. We construct solutions for vanishing and non-vanishing symmetry preserving dilaton potentials. The solutions assemble the pre- and post-big bang evolutions in one single line element. Our results show a smooth evolution from an anisotropic early stage to an isotropic phase without any special initial conditions in contrast to previous models. In addition, we demonstrate that the contraction of the dual space automatically leads to both an inflation phase and a decelerated expansion of the ordinary space during different evolution stages.
Introducing Group Theory through Music
ERIC Educational Resources Information Center
Johnson, Craig M.
2009-01-01
The central ideas of postcalculus mathematics courses offered in college are difficult to introduce in middle and secondary schools, especially through the engineering and sciences examples traditionally used in algebra, geometry, and trigonometry textbooks. However, certain concepts in music theory can be used to expose students to interesting…
String theory in electromagnetic fields
NASA Astrophysics Data System (ADS)
Ambjørn, Jan; Makeenko, Yuri M.; Semenoff, Gordon W.; Szabo, Richard J.
2003-02-01
A review of various aspects of superstrings in background electromagnetic fields is presented. Topics covered include the Born-Infeld action, spectrum of open strings in background gauge fields, the Schwinger mechanism, finite-temperature formalism and Hagedorn behaviour in external fields, Debye screening, D-brane scattering, thermodynamics of D-branes, and noncommutative field and string theories on D-branes. The electric field instabilities are emphasized throughout and contrasted with the case of magnetic fields. A new derivation of the velocity-dependent potential between moving D-branes is presented, as is a new result for the velocity corrections to the one-loop thermal effective potential.
On supersymmetric Lifshitz field theories
NASA Astrophysics Data System (ADS)
Chapman, Shira; Oz, Yaron; Raviv-Moshe, Avia
2015-10-01
We consider field theories that exhibit a supersymmetric Lifshitz scaling with two real supercharges. The theories can be formulated in the language of stochastic quan-tization. We construct the free field supersymmetry algebra with rotation singlet fermions for an even dynamical exponent z = 2 k in an arbitrary dimension. We analyze the classical and quantum z = 2 supersymmetric interactions in 2 + 1 and 3 + 1 spacetime dimensions and reveal a supersymmetry preserving quantum diagrammatic cancellation. Stochastic quantization indicates that Lifshitz scale invariance is broken in the (3 + 1)-dimensional quantum theory.
NASA Astrophysics Data System (ADS)
Weinberg, Steven
1996-08-01
In this second volume of The Quantum Theory of Fields, available for the first time in paperback, Nobel Laureate Steven Weinberg continues his masterly expoistion of quantum theory. Volume 2 provides an up-to-date and self-contained account of the methods of quantum field theory, and how they have led to an understanding of the weak, strong, and electromagnetic interactions of the elementary particles. The presentation of modern mathematical methods is throughout interwoven with accounts of the problems of elementary particle physics and condensed matter physics to which they have been applied. Exercises are included at the end of each chapter.
Understanding conformal field theory through parafermions and Chern Simons theory
Hotes, S.A.
1992-11-19
Conformal field theories comprise a vast class of exactly solvable two dimensional quantum field theories. Conformal theories with an enlarged symmetry group, the current algebra symmetry, axe a key ingredient to possible string compactification models. The following work explores a Lagrangian approach to these theories. In the first part of this thesis, a large class of conformal theories, the so-called coset models, are derived semi-classically from a gauged version Of the Wess-Zumino-Witten functional. A non-local field transformation to the parafermionic field description is employed in the quantization procedure. Classically, these parafermionic fields satisfy non-trivial Poisson brackets, providing insight into the fractional spin nature of the conformal theory. The W-algebra symmetry is shown to appear naturally in this approach. In the second part of this thesis, the connection between the fusion algebra structure of Wess-Zumino-Witten models and the quantization of the Chern-Simons action on the torus is made explicit. The modular properties of the conformal model are also derived in this context, giving a natural demonstration of the Verlinde conjecture. The effects of background gauge fields and monopoles are also discussed.
Group Development: Extending Tuckman's Theory.
ERIC Educational Resources Information Center
Maples, Mary F.
1988-01-01
Presents a framework for extending the Tuckman model of developmental sequence in small groups. Considers Tuckman's stages of forming, storming, norming, performing, and adjourning lacking in descriptive depth and clear definition. Gathered and organized group dynamics graduate students' assessments of characteristics of stages over five-year…
Nonlocal and quasilocal field theories
NASA Astrophysics Data System (ADS)
Tomboulis, E. T.
2015-12-01
We investigate nonlocal field theories, a subject that has attracted some renewed interest in connection with nonlocal gravity models. We study, in particular, scalar theories of interacting delocalized fields, the delocalization being specified by nonlocal integral kernels. We distinguish between strictly nonlocal and quasilocal (compact support) kernels and impose conditions on them to insure UV finiteness and unitarity of amplitudes. We study the classical initial value problem for the partial integro-differential equations of motion in detail. We give rigorous proofs of the existence but accompanying loss of uniqueness of solutions due to the presence of future, as well as past, "delays," a manifestation of acausality. In the quantum theory we derive a generalization of the Bogoliubov causality condition equation for amplitudes, which explicitly exhibits the corrections due to nonlocality. One finds that, remarkably, for quasilocal kernels all acausal effects are confined within the compact support regions. We briefly discuss the extension to other types of fields and prospects of such theories.
Renormalizability of supersymmetric group field cosmology
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker
2014-03-01
In this paper we consider the gauge invariant third quantized model of supersymmetric group field cosmology. The supersymmetric BRST invariance for such theory in non-linear gauge is also analysed. The path integral formulation to the case of a multiverse made up of homogeneous and isotropic spacetimes filled with a perfect fluid is presented. The renormalizability for the scattering of universes in multiverse are established with suitably constructed master equations for connected diagrams and proper vertices. The Slavnov-Taylor identities for this theory hold to all orders of radiative corrections.
Field-theory methods in coagulation theory
Lushnikov, A. A.
2011-08-15
Coagulating systems are systems of chaotically moving particles that collide and coalesce, producing daughter particles of mass equal to the sum of the masses involved in the respective collision event. The present article puts forth basic ideas underlying the application of methods of quantum-field theory to the theory of coagulating systems. Instead of the generally accepted treatment based on the use of a standard kinetic equation that describes the time evolution of concentrations of particles consisting of a preset number of identical objects (monomers in the following), one introduces the probability W(Q, t) to find the system in some state Q at an instant t for a specific rate of transitions between various states. Each state Q is characterized by a set of occupation numbers Q = (n{sub 1}, n{sub 2}, ..., n{sub g}, ...), where n{sub g} is the total number of particles containing precisely g monomers. Thereupon, one introduces the generating functional {Psi} for the probability W(Q, t). The time evolution of {Psi} is described by an equation that is similar to the Schroedinger equation for a one-dimensional Bose field. This equation is solved exactly for transition rates proportional to the product of the masses of colliding particles. It is shown that, within a finite time interval, which is independent of the total mass of the entire system, a giant particle of mass about the mass of the entire system may appear in this system. The particle in question is unobservable in the thermodynamic limit, and this explains the well-known paradox of mass-concentration nonconservation in classical kinetic theory. The theory described in the present article is successfully applied in studying the time evolution of random graphs.
Lectures on Crystal Field Theory
1982-11-01
used to calculate the electric dipole transition probabilities using the theory of Judd (1962) and Ofelt (1962)o As of 1970, all these objectives had...metry higher than C1 or C•. (4) The calculation of transltion probabilities, Zeeman splitting factors, Judd - Ofelt intensity parameters, branching ratios...INTERACTIONS ..................................... 37 4.1 Phenomenological Theory of Crystal Fields ................ 37 4.1.1 Matrix Elements of H in J States
Fornace, Mark E; Lee, Joonho; Miyamoto, Kaito; Manby, Frederick R; Miller, Thomas F
2015-02-10
We introduce embedded mean-field theory (EMFT), an approach that flexibly allows for the embedding of one mean-field theory in another without the need to specify or fix the number of particles in each subsystem. EMFT is simple, is well-defined without recourse to parameters, and inherits the simple gradient theory of the parent mean-field theories. In this paper, we report extensive benchmarking of EMFT for the case where the subsystems are treated using different levels of Kohn-Sham theory, using PBE or B3LYP/6-31G* in the high-level subsystem and LDA/STO-3G in the low-level subsystem; we also investigate different levels of density fitting in the two subsystems. Over a wide range of chemical problems, we find EMFT to perform accurately and stably, smoothly converging to the high-level of theory as the active subsystem becomes larger. In most cases, the performance is at least as good as that of ONIOM, but the advantages of EMFT are highlighted by examples that involve partitions across multiple bonds or through aromatic systems and by examples that involve more complicated electronic structure. EMFT is simple and parameter free, and based on the tests provided here, it offers an appealing new approach to a multiscale electronic structure.
Computer Programming and Group Theory
1990-05-01
the following: SO is the null subgroup S1 = ( eO el e2 ) The above was a very quick walk -through of the group generation options of the system. We will...depth-of-canonical form) first element - canionical form~m] En]; hold =n; ++n; while(canionicatlform(m][n] I 1 \\0’) if(first-element > canonical...canonicalform - 0) m z 0; first element = canonical forin~m] En]; hold = m; ++m; while(m :depth of canionical form) if(first-element < canonical-formlm
Group target tracking using game theory
NASA Astrophysics Data System (ADS)
Sadjadi, Firooz A.; Kober, Wolfgang
2001-10-01
The problem of tracking of a group of targets is considered in this paper. We will present an overview of an investigation into this problem by first using the targets velocity state vectors covariance matrix to establish target grouping and then by exploiting concepts derived from game theory, in particular the leader-follower techniques, and graph theory to represent and establish relationships that influence the tracking of objects that belong to a group formation.
Unitarity of superstring field theory
NASA Astrophysics Data System (ADS)
Sen, Ashoke
2016-12-01
We complete the proof of unitarity of (compactified) heterotic and type II string field theories by showing that in the cut diagrams only physical states appear in the sum over intermediate states. This analysis takes into account the effect of mass and wave-function renormalization, and the possibility that the true vacuum may be related to the perturbative vacuum by small shifts in the string fields.
Charge transfer in algebraic quantum field theory
NASA Astrophysics Data System (ADS)
Wright, Jill Dianne
We discuss aspects of the algebraic structure of quantum field theory. We take the view that the superselection structure of a theory should be determinable from the vacuum representation of the observable algebra, and physical properties of the charge. Hence one determines the nature of the charge transfer operations: the automorphisms of the observable algebra corresponding to the movement of charge along space-time paths. New superselection sectors are obtained from the vacuum sector by an automorphism which is a limit of charge transfer operations along paths with an endpoint tending to spacelike infinity. Roberts has shown that for a gauge theory of the first kind, the charge transfer operations for a given charge form a certain kind of 1-cocycle over Minkowski space. The local 1-cohomology group of their equivalence classes corresponds to the superselection structure. The exact definition of the cohomology group depends on the properties of the charge. Using displaced Fock representations of free fields, we develop model field theories which illustrate this structure. The cohomological classification of displaced Fock representations has been elucidated by Araki. For more general representations, explicit determination of the cohomology group is a hard problem. Using our models, we can illustrate ways in which fields with reasonable physical properties depart fromthe abovementioned structure. In 1+1 dimensions, we use the Streater-Wilde model to illustrate explicitly the representation-dependence of the cohomology structure, and the direction-dependence of the limiting charge transfer operation. The cohomology structure may also be representation-dependent in higher-dimensional theories without strict localization of charge, for example the electromagnetic field. The algebraic structure of the electromagnetic field has many other special features, which we discuss in relation to the concept of charge transfer. We also give some indication of the modifications
Noncommutative Geometry in M-Theory and Conformal Field Theory
Morariu, Bogdan
1999-05-01
In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U_{q}(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun_{q} (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.
Transpersonal Group Psychotherapy: Theory, Method, and Community.
ERIC Educational Resources Information Center
Clark, Carlton F. "Perk"
1998-01-01
Transpersonal group psychotherapy is a carpet of theory, technique, and experiences woven from threads of contemporary psychology, mysticism, and a perennial philosophy many centuries old. Introduces the basic concepts of transpersonal group psychotherapy, proposes a model of transpersonal group psychotherapy, discusses the training of…
Introduction to string theory and conformal field theory
Belavin, A. A. Tarnopolsky, G. M.
2010-05-15
A concise survey of noncritical string theory and two-dimensional conformal field theory is presented. A detailed derivation of a conformal anomaly and the definition and general properties of conformal field theory are given. Minimal string theory, which is a special version of the theory, is considered. Expressions for the string susceptibility and gravitational dimensions are derived.
Variational methods for field theories
NASA Astrophysics Data System (ADS)
Ben-Menahem, Shahar
1986-09-01
The thesis is presented in four parts dealing with field theory models: Periodic Quantum Electrodynamics (PQED) in (2+1) dimensions, free scalar field theory in (1+1) dimensions, the Quantum XY model in (1+1) dimensions, and the (1+1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. Free field theory is used as a laboratory for a new variational blocking truncation approximation, in which the high frequency modes in a block are truncated to wave functions that depend on the slower background model (Born Oppenheimer approximation). For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. In the 4th part, the transfer matrix method is used to find a good (non blocking) trial ground state for the Ising model in a transverse magnetic field in (1+1) dimensions.
Theory Loves Practice: A Teacher Researcher Group
ERIC Educational Resources Information Center
Hochtritt, Lisa; Thulson, Anne; Delaney, Rachael; Dornbush, Talya; Shay, Sarah
2014-01-01
Once a month, art educators from the Denver metro area have been gathering together in the spirit of inquiry to explore issues of the perceived theory and daily practice divide. The Theory Loves Practice (TLP) group was started in 2010 by Professors Rachael Delaney and Anne Thulson from Metropolitan State University of Denver (MSU) and now has 40…
Bohmian mechanics and quantum field theory.
Dürr, Detlef; Goldstein, Sheldon; Tumulka, Roderich; Zanghì, Nino
2004-08-27
We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end.
Variational methods for field theories
Ben-Menahem, S.
1986-09-01
Four field theory models are studied: Periodic Quantum Electrodynamics (PQED) in (2 + 1) dimensions, free scalar field theory in (1 + 1) dimensions, the Quantum XY model in (1 + 1) dimensions, and the (1 + 1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path-integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. This includes a better quantitative agreement for the string tensions in the two approaches. Free field theory is used as a laboratory for a new variational blocking-truncation approximation, in which the high-frequency modes in a block are truncated to wave functions that depend on the slower background modes (Boron-Oppenheimer approximation). This ''adiabatic truncation'' method gives very accurate results for ground-state energy density and correlation functions. Various adiabatic schemes, with one variable kept per site and then two variables per site, are used. For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. A connection is established with the vortex Coulomb gas of the Euclidean path integral approach. The approximations used are taken from the realms of statistical mechanics (mean field approximation, transfer-matrix methods) and of quantum mechanics (iterative blocking schemes). In developing blocking schemes based on continuous variables, problems due to the periodicity of the model were solved. Our results exhibit an order-disorder phase transition. The transfer-matrix method is used to find a good (non-blocking) trial ground state for the Ising model in a transverse magnetic field in (1 + 1) dimensions.
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro
2015-09-02
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.« less
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro E-mail: mwhite@berkeley.edu
2015-09-01
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The 'new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all of our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. All the perturbative models fare better than linear theory.
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro
2015-09-02
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all of our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.
NASA Astrophysics Data System (ADS)
Karkheck, John; Stell, George
1981-08-01
A kinetic mean-field theory for the evolution of the one-particle distribution function is derived from maximizing the entropy. For a potential with a hard-sphere core plus tail, the resulting theory treats the hard-core part as in the revised Enskog theory. The tail, weighted by the hard-sphere pair distribution function, appears linearly in a mean-field term. The kinetic equation is accompanied by an entropy functional for which an H theorem was proven earlier. The revised Enskog theory is obtained by setting the potential tail to zero, the Vlasov equation is obtained by setting the hard-sphere diameter to zero, and an equation of the Enskog-Vlasov type is obtained by effecting the Kac limit on the potential tail. At equilibrium, the theory yields a radial distribution function that is given by the hard-sphere reference system and thus furnishes through the internal energy a thermodynamic description which is exact to first order in inverse temperature. A second natural route to thermodynamics (from the momentum flux which yields an approximate equation of state) gives somewhat different results; both routes coincide and become exact in the Kac limit. Our theory furnishes a conceptual basis for the association in the heuristically based modified Enskog theory (MET) of the contact value of the radial distribution function with the ''thermal pressure'' since this association follows from our theory (using either route to thermodynamics) and moreover becomes exact in the Kac limit. Our transport theory is readily extended to the general case of a soft repulsive core, e.g., as exhibited by the Lennard-Jones potential, via by-now-standard statistical-mechanical methods involving an effective hard-core potential, thus providing a self-contained statistical-mechanical basis for application to such potentials that is lacking in the standard versions of the MET. We obtain very good agreement with experiment for the thermal conductivity and shear viscosity of several
Symplectic Clifford Algebraic Field Theory.
NASA Astrophysics Data System (ADS)
Dixon, Geoffrey Moore
We develop a mathematical framework on which is built a theory of fermion, scalar, and gauge vector fields. This field theory is shown to be equivalent to the original Weinberg-Salam model of weak and electromagnetic interactions, but since the new framework is more rigid than that on which the original Weinberg-Salam model was built, a concomitant reduction in the number of assumptions lying outside of the framework has resulted. In particular, parity violation is actually hiding within our framework, and with little difficulty we are able to manifest it. The mathematical framework upon which we build our field theory is arrived at along two separate paths. The first is by the marriage of a Clifford algebra and a Lie superalgebra, the result being called a super Clifford algebra. The second is by providing a new characterization for a Clifford algebra employing its generators and a symmetric array of metric coefficients. Subsequently we generalize this characterization to the case of an antisymmetric array of metric coefficients, and we call the algebra which results a symplectic Clifford algebra. It is upon one of these that we build our field theory, and it is shown that this symplectic Clifford algebra is a particular subalgebra of a super Clifford algebra. The final ingredient is the operation of bracketing which involves treating the elements of our algebra as endomorphisms of a particular inner product space, and employing this space and its inner product to provide us with maps from our algebra to the reals. It is this operation which enables us to manifest the parity violation hiding in our algebra.
Symmetries in Lagrangian Field Theory
NASA Astrophysics Data System (ADS)
Búa, Lucia; Bucataru, Ioan; León, Manuel de; Salgado, Modesto; Vilariño, Silvia
2015-06-01
By generalising the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first-order jet bundles J1π of a fiber bundle π : E → ℝk where ℝk is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether theorem is proved.
A Review of Group Systems Theory
ERIC Educational Resources Information Center
Connors, Joanie V.; Caple, Richard B.
2005-01-01
The ability to see interpersonal and group processes beyond the individual level is an essential skill for group therapists (Crouch, Bloch & Wanlass, 1994; Dies, 1994; Fuhriman & Burlingame, 1994). In addition to interpersonal therapy models (e.g., Sullivan and Yalom), there are a number of systems theory models that offer a broad array of…
Group Theory of Covariant Harmonic Oscillators
ERIC Educational Resources Information Center
Kim, Y. S.; Noz, Marilyn E.
1978-01-01
A simple and concrete example for illustrating the properties of noncompact groups is presented. The example is based on the covariant harmonic-oscillator formalism in which the relativistic wave functions carry a covariant-probability interpretation. This can be used in a group theory course for graduate students who have some background in…
Group Chaos Theory: A Metaphor and Model for Group Work
ERIC Educational Resources Information Center
Rivera, Edil Torres; Wilbur, Michael; Frank-Saraceni, James; Roberts-Wilbur, Janice; Phan, Loan T.; Garrett, Michael T.
2005-01-01
Group phenomena and interactions are described through the use of the chaos theory constructs and characteristics of sensitive dependence on initial conditions, phase space, turbulence, emergence, self-organization, dissipation, iteration, bifurcation, and attractors and fractals. These constructs and theoretical tenets are presented as applicable…
Changing Views of Quantum Field Theory
NASA Astrophysics Data System (ADS)
Weinberg, Steven
2010-03-01
The first part of this talk reviews changes in our views regarding quantum field theory since its beginnings, leading eventually to the modern view that our most successful field theories may in fact be effective field theories, valid only as low energy approximations to an underlying theory that may not be a field theory at all. In the second part, I reminisce about the early development of effective field theories of the strong interactions, comment briefly on some other applications of effective field theories, then take up the idea that the Standard Model and General Relativity are the leading terms in an effective field theory, and finally cite recent calculations that suggest that the effective field theory of gravitation and matter is asymptotically safe. The second part is substantially the same as a talk given a month earlier at the 6th International Workshop on Chiral Dynamics, at the University of Bern, which is reproduced here.
Effective Particles in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Głazek, Stanisław D.; Trawiński, Arkadiusz P.
2017-03-01
The concept of effective particles is introduced in the Minkowski space-time Hamiltonians in quantum field theory using a new kind of the relativistic renormalization group procedure that does not integrate out high-energy modes but instead integrates out the large changes of invariant mass. The new procedure is explained using examples of known interactions. Some applications in phenomenology, including processes measurable in colliders, are briefly presented.
Integrable structures in quantum field theory
NASA Astrophysics Data System (ADS)
Negro, Stefano
2016-08-01
This review was born as notes for a lecture given at the Young Researchers Integrability School (YRIS) school on integrability in Durham, in the summer of 2015. It deals with a beautiful method, developed in the mid-nineties by Bazhanov, Lukyanov and Zamolodchikov and, as such, called BLZ. This method can be interpreted as a field theory version of the quantum inverse scattering, also known as the algebraic Bethe ansatz. Starting with the case of conformal field theories (CFTs) we show how to build the field theory analogues of commuting transfer T matrices and Baxter Q-operators of integrable lattice models. These objects contain the complete information of the integrable structure of the theory, viz. the integrals of motion, and can be used, as we will show, to derive the thermodynamic Bethe ansatz and nonlinear integral equations. This same method can be easily extended to the description of integrable structures of certain particular massive deformations of CFTs; these, in turn, can be described as quantum group reductions of the quantum sine-Gordon model and it is an easy step to include this last theory in the framework of BLZ approach. Finally we show an interesting and surprising connection of the BLZ structures with classical objects emerging from the study of classical integrable models via the inverse scattering transform method. This connection goes under the name of ODE/IM correspondence and we will present it for the specific case of quantum sine-Gordon model only.
Gauge Field Theories, 2nd Edition
NASA Astrophysics Data System (ADS)
Frampton, Paul H.
2000-08-01
The first edition of Gauge Field Theories, published in 1985, quickly became widely used in universities and other institutions of higher learning around the world. Written by well-known physicist Paul Frampton, the new edition continues to offer a first-rate mathematical treatment of gauge field theories, while thoroughly updating all chapters to keep pace with developments in the field. Frampton emphasizes formalism rather than experiments and provides sufficient detail for readers wishing to do their own calculations or pursue theoretical physics research. Special features of the Second Edition include: * Improved, logical organization of the material on gauge invariance, quantization, and renormalization * Major revision of the chapter on electroweak interactions, incorporating the latest precision data and discovery of the top quark * Discussions of renormalization group and quantum chromodynamics * A completely new chapter on model building
Variational Methods for Field Theories.
NASA Astrophysics Data System (ADS)
Ben-Menahem, Shahar
The thesis has four parts, dealing with four field theory models: Periodic Quantum Electrodynamics (PQED) in (2 + 1) dimensions, free scalar field theory in (1 + 1) dimensions, the Quantum XY model in (1 + 1) dimensions, and the (1 + 1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path-integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. This includes a better quantitative agreement for the string tensions in the two approaches. In the second part, we use free field theory as a loboratory for a new variational blocking-tuncation approximation, in which the high-frequency modes in a block are truncated to wave functions that depend on the slower background modes(Born-Oppenheimer approximation). This "adiabatic truncation" method gives very accurate results for ground -state energy density and correlation functions. Without the adiabatic method, a much larger number of state per block must be kept to get comparable results. Various adiabatic schemes, with one variable kept per site and then two variables per site, are used. For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. A connection is established with the vortex Coulomb gas of the Eclidean path integral approach. The approximations used are taken from the realms of statistical mechanics (mean field approximation, transfer-matrix methods) and of quantum mechanics (iterative blocking schemes). In developing blocking schemes based on continuous variables, problems due to the periodicity of the model were solved. Our results exhibit an order-disorder phase transition. This transition is a rudimentary version of the actual transition known to occur in the XY model, and is
Field Analysis and Potential Theory
1985-06-01
distance measured from a point singularity P, then the total source strength associated with a neighbourhood of P remains finite if foIt’ n is bounded...a neighbourhood of the source, where it takes the form ii 296 FIELD ANALYSIS AND POTENTIAL THEORY [Sec.4.11 T- 1k + U where r’ is distance measured ...8217,t) + f2(x~yzt) in a neighbourhood of the point P, where r’ is distance measured from P and fj and f 2 are well-behaved functions of space and time
Topics in low-dimensional field theory
Crescimanno, M.J.
1991-04-30
Conformal field theory is a natural tool for understanding two- dimensional critical systems. This work presents results in the lagrangian approach to conformal field theory. The first sections are chiefly about a particular class of field theories called coset constructions and the last part is an exposition of the connection between two-dimensional conformal theory and a three-dimensional gauge theory whose lagrangian is the Chern-Simons density.
Haag's theorem in noncommutative quantum field theory
Antipin, K. V.; Mnatsakanova, M. N.; Vernov, Yu. S.
2013-08-15
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
Euclidean quantum field theory: Curved spacetimes and gauge fields
NASA Astrophysics Data System (ADS)
Ritter, William Gordon
This thesis presents a new formulation of quantum field theory (QFT) on curved spacetimes, with definite advantages over previous formulations, and an introduction to the millennium prize problem on four-dimensional gauge theory. Our constructions are completely rigorous, making QFT on curved spacetimes into a subfield of mathematics, and we achieve the first analytic control over nonperturbative aspects of interacting theories on curved spacetimes. The success of Euclidean path integrals to capture nonperturbative aspects of QFT has been striking. The Euclidean path integral is the most accurate method of calculating strong-coupling effects in gauge theory (such as glueball masses). Euclidean methods are also useful in the study of black holes, as evidenced by the Hartle-Hawking calculation of black-hole radiance. From a mathematical point of view, on flat spacetimes the Euclidean functional integral provides the most elegant method of constructing examples of interacting relativistic field theories. Yet until now, the incredibly-useful Euclidean path integral had never been given a definitive mathematical treatment on curved backgrounds. It is our aim to rectify this situation. Along the way, we discover that the Dirac operator on an arbitrary Clifford bundle has a resolvent kernel which is the Laplace transform of a positive measure. In studying spacetime symmetries, we discover a new way of constructing unitary representations of noncompact Lie groups. We also define and explore an interesting notion of convergence for Laplacians. The same mathematical framework applies to scalar fields, fermions, and gauge fields. The later chapters are devoted to gauge theory. We present a rigorous, self-contained introduction to the subject, aimed at mathematicians and using the language of modern mathematics, with a view towards nonperturbative renormalization in four dimensions. The latter ideas are unfinished. A completion of the final chapter would imply the construction
Small-Group Instruction. Theory and Practice
1974-01-01
Human Relations, vol. 1, 1948, cation Association, Washington, pp. 512-532. 1961, pp. 34-47, 125 Preceding Page Blank References 21. Cartwright , Dorwin ...Rela- Membership," in Dorwin Cartwright tions and Administration, Harvard and A. Zander (eds,), Group University Press, Cambridge, Mass., Dynamics... Dorwin Cartwright and A. 54. Johnson, D.M., and Smith, H.C. Zander (eds.) Group Dynamics: "Democratic Leadership in the Research and Theory, Row
From operator algebras to superconformal field theory
Kawahigashi, Yasuyuki
2010-01-15
We survey operator algebraic approach to (super)conformal field theory. We discuss representation theory, classification results, full and boundary conformal field theories, relations to supervertex operator algebras and Moonshine, connections to subfactor theory of Jones, and certain aspects of noncommutative geometry of Connes.
Teaching Group Theory Using Rubik's Cubes
ERIC Educational Resources Information Center
Cornock, Claire
2015-01-01
Being situated within a course at the applied end of the spectrum of maths degrees, the pure mathematics modules at Sheffield Hallam University have an applied spin. Pure topics are taught through consideration of practical examples such as knots, cryptography and automata. Rubik's cubes are used to teach group theory within a final year pure…
Field Theory of Fundamental Interactions
NASA Astrophysics Data System (ADS)
Wang, Shouhong; Ma, Tian
2017-01-01
First, we present two basic principles, the principle of interaction dynamics (PID) and the principle of representation invariance (PRI). Intuitively, PID takes the variation of the action under energy-momentum conservation constraint. We show that the PID is the requirement of the presence of dark matter and dark energy, the Higgs field and the quark confinement. PRI requires that the SU(N) gauge theory be independent of representations of SU(N). It is clear that PRI is the logic requirement of any gauge theory. With PRI, we demonstrate that the coupling constants for the strong and the weak interactions are the main sources of these two interactions, reminiscent of the electric charge. Second, we emphasize that symmetry principles-the principle of general relativity and the principle of Lorentz invariance and gauge invariance-together with the simplicity of laws of nature, dictate the actions for the four fundamental interactions. Finally, we show that the PID and the PRI, together with the symmetry principles give rise to a unified field model for the fundamental interactions, which is consistent with current experimental observations and offers some new physical predictions. The research is supported in part by the National Science Foundation (NSF) grant DMS-1515024, and by the Office of Naval Research (ONR) grant N00014-15-1-2662.
Quantum Field Theory in (0 + 1) Dimensions
ERIC Educational Resources Information Center
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
The Construction of Group Theory in Crystallography
NASA Astrophysics Data System (ADS)
Maitte, Bernard
This article sets out to retrace the manner in which Group Theory evolved in crystallography. To engage in this study it is necessary to select, amongst all the approaches to crystals, those which, from the point of view of modern science, mark a step towards the establishment of our current understanding. In this way it favours our current perspective. To compensate this distortion, we recall the context in which each explanation that marks history appears. It so becomes clear that notions of triperiodic assemblages and the crystallographic laws of crystal systems and symmetrical classes do not derive from "natural" observations but were compiled and belong to precise theories.
Logarithmic conformal field theory: beyond an introduction
NASA Astrophysics Data System (ADS)
Creutzig, Thomas; Ridout, David
2013-12-01
of the underlying chiral algebra and the modular data pertaining to the characters of the representations. Each of the archetypal logarithmic conformal field theories is studied here by first determining its irreducible spectrum, which turns out to be continuous, as well as a selection of natural reducible, but indecomposable, modules. This is followed by a detailed description of how to obtain character formulae for each irreducible, a derivation of the action of the modular group on the characters, and an application of the Verlinde formula to compute the Grothendieck fusion rules. In each case, the (genuine) fusion rules are known, so comparisons can be made and favourable conclusions drawn. In addition, each example admits an infinite set of simple currents, hence extended symmetry algebras may be constructed and a series of bulk modular invariants computed. The spectrum of such an extended theory is typically discrete and this is how the triplet model \\mathfrak {W} (1,2) arises, for example. Moreover, simple current technology admits a derivation of the extended algebra fusion rules from those of its continuous parent theory. Finally, each example is concluded by a brief description of the computation of some bulk correlators, a discussion of the structure of the bulk state space, and remarks concerning more advanced developments and generalizations. The final part gives a very short account of the theory of staggered modules, the (simplest class of) representations that are responsible for the logarithmic singularities that distinguish logarithmic theories from their rational cousins. These modules are discussed in a generality suitable to encompass all the examples met in this review and some of the very basic structure theory is proven. Then, the important quantities known as logarithmic couplings are reviewed for Virasoro staggered modules and their role as fundamentally important parameters, akin to the three-point constants of rational conformal field
Differential geometry of groups in string theory
Schmidke, W.B. Jr.
1990-09-01
Techniques from differential geometry and group theory are applied to two topics from string theory. The first topic studied is quantum groups, with the example of GL (1{vert bar}1). The quantum group GL{sub q}(1{vert bar}1) is introduced, and an exponential description is derived. The algebra and coproduct are determined using the invariant differential calculus method introduced by Woronowicz and generalized by Wess and Zumino. An invariant calculus is also introduced on the quantum superplane, and a representation of the algebra of GL{sub q}(1{vert bar}1) in terms of the super-plane coordinates is constructed. The second topic follows the approach to string theory introduced by Bowick and Rajeev. Here the ghost contribution to the anomaly of the energy-momentum tensor is calculated as the Ricci curvature of the Kaehler quotient space Diff(S{sup 1})/S{sup 1}. We discuss general Kaehler quotient spaces and derive an expression for their Ricci curvatures. Application is made to the string and superstring diffeomorphism groups, considering all possible choices of subgroup. The formalism is extended to associated holomorphic vector bundles, where the Ricci curvature corresponds to the anomaly for different ghost sea levels. 26 refs.
Quantum Mechanics and Quantum Field Theory
NASA Astrophysics Data System (ADS)
Dimock, Jonathan
2011-02-01
Introduction; Part I. Non-relativistic: 1. Mathematical prelude; 2. Classical mechanics; 3. Quantum mechanics; 4. Single particle; 5. Many particles; 6. Statistical mechanics; Part II. Relativistic: 7. Relativity; 8. Scalar particles and fields; 9. Electrons and photons; 10. Field theory on a manifold; Part III. Probabilistic Methods: 11. Path integrals; 12. Fields as random variables; 13. A nonlinear field theory; Appendices; References; Index.
Supersymmetric extensions of K field theories
NASA Astrophysics Data System (ADS)
Adam, C.; Queiruga, J. M.; Sanchez-Guillen, J.; Wereszczynski, A.
2012-02-01
We review the recently developed supersymmetric extensions of field theories with non-standard kinetic terms (so-called K field theories) in two an three dimensions. Further, we study the issue of topological defect formation in these supersymmetric theories. Specifically, we find supersymmetric K field theories which support topological kinks in 1+1 dimensions as well as supersymmetric extensions of the baby Skyrme model for arbitrary nonnegative potentials in 2+1 dimensions.
Palmer, R.B.; Baggett, N.; Claus, J.; Fernow, R.; Stumer, I.; Figueroa, H.; Kroll, N.; Funk, W.; Lee-Whiting, G.; Pickup, M.
1985-04-01
Substantial progress since the Los Alamos Workshop two years ago is reported. A radio-frequency model of a grating accelerator has been tested at Cornell, and extensive calculations compared with observations. Alternative structures consisting of either hemispherical bumps on a plane, or conducting spheres in space, have also been rf modeled. The use of liquid droplets to form such structures has been proposed and a conceptual design studied. Calculations and experiments have examined the effects of surface plasmas, and shown that in this case the reflectivity is low. However, calculations and observations suggest that gradients in excess of 1 GeV/meter should be obtainable without forming such plasma. An examination of wake fields shows that, with Landau damping, these are independent of wavelength. The use of near field structures to act as high gradient focusing elements has been studied and shows promise, independent of the acceleration mechanism. A proposal has been made to establish a facility that would enable ''proof of principle experiments'' to be performed on these and other laser driven accelerator mechanisms. 11 refs., 10 figs.
On the global symmetries of 6D superconformal field theories
NASA Astrophysics Data System (ADS)
Bertolini, Marco; Merkx, Peter R.; Morrison, David R.
2016-07-01
We study global symmetry groups of six-dimensional superconformal field theories (SCFTs). In the Coulomb branch we use field theoretical arguments to predict an upper bound for the global symmetry of the SCFT. We then analyze global symmetry groups of F-theory constructions of SCFTs with a one-dimensional Coulomb branch. While in the vast majority of cases, all of the global symmetries allowed by our Coulomb branch analysis can be realized in F-theory, in a handful of cases we find that F-theory models fail to realize the full symmetry of the theory on the Coulomb branch. In one particularly mysterious case, F-theory models realize several distinct maximal subgroups of the predicted group, but not the predicted group itself.
Groups, information theory, and Einstein's likelihood principle
NASA Astrophysics Data System (ADS)
Sicuro, Gabriele; Tempesta, Piergiulio
2016-04-01
We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the Shannon-Khinchin axioms. We associate to each member of a large class of entropies a generalized information measure, satisfying the additivity property on a set of independent systems as a consequence of the underlying group law. At the same time, we also show that Einstein's likelihood function naturally emerges as a byproduct of our informational interpretation of (generally nonadditive) entropies. These results confirm the adequacy of composable entropies both in physical and social science contexts.
Groups, information theory, and Einstein's likelihood principle.
Sicuro, Gabriele; Tempesta, Piergiulio
2016-04-01
We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the Shannon-Khinchin axioms. We associate to each member of a large class of entropies a generalized information measure, satisfying the additivity property on a set of independent systems as a consequence of the underlying group law. At the same time, we also show that Einstein's likelihood function naturally emerges as a byproduct of our informational interpretation of (generally nonadditive) entropies. These results confirm the adequacy of composable entropies both in physical and social science contexts.
Toward a gauge field theory of gravity.
NASA Astrophysics Data System (ADS)
Yilmaz, H.
Joint use of two differential identities (Bianchi and Freud) permits a gauge field theory of gravity in which the gravitational energy is localizable. The theory is compatible with quantum mechanics and is experimentally viable.
Common Group Problems: A Field Study.
ERIC Educational Resources Information Center
Weinberg, Sanford B.; And Others
1981-01-01
A field study of a naturally functioning group (N=125) was conducted to identify common group problems. Trained observers attended group meetings and described the problems encountered. Difficulties of cohesion, leadership, sub-group formation, and personality conflict were identified. (RC)
Group theoretical methods and wavelet theory: coorbit theory and applications
NASA Astrophysics Data System (ADS)
Feichtinger, Hans G.
2013-05-01
Before the invention of orthogonal wavelet systems by Yves Meyer1 in 1986 Gabor expansions (viewed as discretized inversion of the Short-Time Fourier Transform2 using the overlap and add OLA) and (what is now perceived as) wavelet expansions have been treated more or less at an equal footing. The famous paper on painless expansions by Daubechies, Grossman and Meyer3 is a good example for this situation. The description of atomic decompositions for functions in modulation spaces4 (including the classical Sobolev spaces) given by the author5 was directly modeled according to the corresponding atomic characterizations by Frazier and Jawerth,6, 7 more or less with the idea of replacing the dyadic partitions of unity of the Fourier transform side by uniform partitions of unity (so-called BUPU's, first named as such in the early work on Wiener-type spaces by the author in 19808). Watching the literature in the subsequent two decades one can observe that the interest in wavelets "took over", because it became possible to construct orthonormal wavelet systems with compact support and of any given degree of smoothness,9 while in contrast the Balian-Low theorem is prohibiting the existence of corresponding Gabor orthonormal bases, even in the multi-dimensional case and for general symplectic lattices.10 It is an interesting historical fact that* his construction of band-limited orthonormal wavelets (the Meyer wavelet, see11) grew out of an attempt to prove the impossibility of the existence of such systems, and the final insight was that it was not impossible to have such systems, and in fact quite a variety of orthonormal wavelet system can be constructed as we know by now. Meanwhile it is established wisdom that wavelet theory and time-frequency analysis are two different ways of decomposing signals in orthogonal resp. non-orthogonal ways. The unifying theory, covering both cases, distilling from these two situations the common group theoretical background lead to the
Teaching group theory using Rubik's cubes
NASA Astrophysics Data System (ADS)
Cornock, Claire
2015-10-01
Being situated within a course at the applied end of the spectrum of maths degrees, the pure mathematics modules at Sheffield Hallam University have an applied spin. Pure topics are taught through consideration of practical examples such as knots, cryptography and automata. Rubik's cubes are used to teach group theory within a final year pure elective based on physical examples. Abstract concepts, such as subgroups, homomorphisms and equivalence relations are explored with the cubes first. In addition to this, conclusions about the cubes can be made through the consideration of algebraic approaches through a process of discovery. The teaching, learning and assessment methods are explored in this paper, along with the challenges and limitations of the methods. The physical use of Rubik's cubes within the classroom and examination will be presented, along with the use of peer support groups in this process. The students generally respond positively to the teaching methods and the use of the cubes.
Scalar field theory on noncommutative Snyder spacetime
Battisti, Marco Valerio; Meljanac, Stjepan
2010-07-15
We construct a scalar field theory on the Snyder noncommutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincare algebra is undeformed. The Lorentz sector is undeformed at both the algebraic and co-algebraic level, but the coproduct for momenta (defining the star product) is non-coassociative. The Snyder-deformed Poincare group is described by a non-coassociative Hopf algebra. The definition of the interacting theory in terms of a nonassociative star product is thus questionable. We avoid the nonassociativity by the use of a space-time picture based on the concept of the realization of a noncommutative geometry. The two main results we obtain are (i) the generic (namely, for any realization) construction of the co-algebraic sector underlying the Snyder geometry and (ii) the definition of a nonambiguous self-interacting scalar field theory on this space-time. The first-order correction terms of the corresponding Lagrangian are explicitly computed. The possibility to derive Noether charges for the Snyder space-time is also discussed.
Generalized approach to global renormalization-group theory for fluids
NASA Astrophysics Data System (ADS)
Ramana, A. Sai Venkata; Menon, S. V. G.
2012-04-01
The global renormalization-group theory (GRGT) for fluids is derived starting with the square-gradient approximation for the Helmholtz free energy functional such that any mean-field free energy density and direct correlation function can be employed. The new derivation uses Wilson's functions for representing density fluctuations, thereby relaxing the assumption of cosine variation of density fluctuations used in earlier approaches. The generality of the present approach is shown by deriving the relationships to the earlier developments. A qualitative way to infer the free parameters in the present form of GRGT is also suggested. The new theory is applied to square-well fluids of ranges 1.5 and 3.0 (in units of hard-sphere diameter) and Lennard-Jones fluids. It is shown that the present theory produces a flat isotherm in the two-phase region. Thus the theory accounts for fluctuations at all length scales and avoids the use of Maxwell's construction. An analysis of the liquid-vapor phase diagrams and the critical constants obtained for different potentials shows that, with a mean-field free energy density that is accurate away from the critical region and an appropriate coarse graining length for the mean-field theory, GRGT can provide results in good agreement with the simulation and experimental results.
Boson formulation of fermion field theories
Ha, Y.K.
1984-04-15
The nonperturbative connection between a canonical Fermi field and a canonical Bose field in two dimensions is developed and its validity verified according to the tenets of quantum field theory. We advocate the point of view that a boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. Many features of the massless theory, such as dynamical mass generation with asymptotic-freedom behavior, hidden chiral symmetry, and connections with models of apparently different internal symmetries, are readily transparent through such fermion-boson metamorphosis.
Bilocal field theory in four dimensions
Hori, T. )
1993-07-15
A bilocal field theory having Moebius gauge invariance is proposed. In four dimensions there exists a zero momentum state of the first-quantized model which belongs to a nontrivial BRS cohomology class. A field theory Lagrangian having gauge invariance only in four dimensions is constructed.
Quantum equivalence of dual field theories
NASA Astrophysics Data System (ADS)
Fradkin, E. S.; Tseytlin, A. A.
1985-06-01
Motivated by the study of ultraviolet properties of different versions of supergravities duality transformations at the quantum level are discussed. Using the background field method it is proven on shell quantum equivalence for several pairs of dual field theories known to be classically equivalent. The examples considered include duality in chiral model, duality of scalars and second rank antisymmetric gauge tensors, vector duality and duality of the Einstein theory with cosmological term and the Eddington-Schrödinger theory.
Pilot-wave theory and quantum fields
NASA Astrophysics Data System (ADS)
Struyve, Ward
2010-10-01
Pilot-wave theories provide possible solutions to the measurement problem. In such theories, quantum systems are not only described by the state vector but also by some additional variables. These additional variables, also called beables, can be particle positions, field configurations, strings, etc. In this paper we focus our attention on pilot-wave theories in which the additional variables are field configurations. The first such theory was proposed by Bohm for the free electromagnetic field. Since Bohm, similar pilot-wave theories have been proposed for other quantum fields. The purpose of this paper is to present an overview and further development of these proposals. We discuss various bosonic quantum field theories such as the Schrödinger field, the free electromagnetic field, scalar quantum electrodynamics and the Abelian Higgs model. In particular, we compare the pilot-wave theories proposed by Bohm and by Valentini for the electromagnetic field, finding that they are equivalent. We further discuss the proposals for fermionic fields by Holland and Valentini. In the case of Holland's model we indicate that further work is required in order to show that the model is capable of reproducing the standard quantum predictions. We also consider a similar model, which does not seem to reproduce the standard quantum predictions. In the case of Valentini's model we point out a problem that seems hard to overcome.
An extremal $${\\mathcal{N}}=2$$ superconformal field theory
Benjamin, Nathan; Dyer, Ethan; Fitzpatrick, A. Liam; ...
2015-11-16
Here, we provide an example of an extremal chiralmore » $${\\mathcal{N}}$$ = 2 superconformal field theory at c = 24. The construction is based on a $${{\\mathbb{Z}}}_{2}$$ orbifold of the theory associated to the $${A}_{1}^{24}$$ Niemeier lattice. The statespace is governed by representations of the sporadic group M 23.« less
An extremal ${\\mathcal{N}}=2$ superconformal field theory
Benjamin, Nathan; Dyer, Ethan; Fitzpatrick, A. Liam; Kachru, Shamit
2015-11-16
Here, we provide an example of an extremal chiral ${\\mathcal{N}}$ = 2 superconformal field theory at c = 24. The construction is based on a ${{\\mathbb{Z}}}_{2}$ orbifold of the theory associated to the ${A}_{1}^{24}$ Niemeier lattice. The statespace is governed by representations of the sporadic group M 23.
Quantum Algorithms for Fermionic Quantum Field Theories
2014-04-28
a theory in two spacetime dimensions with quartic interactions. The algorithm introduces new techniques to meet the additional challenges posed by...in fermionic field theories, exemplified by the massive Gross- Neveu model, a theory in two spacetime dimensions with quartic interactions. The...two spacetime dimensions with quartic interactions. Although our analysis is specific to this theory, our algorithm can be adapted to other massive
Field Equations for Space-Time Theory
NASA Astrophysics Data System (ADS)
Bejancu, Aurel
2013-05-01
In the present paper we obtain, in a covariant form, and in their full generality, the field equations in a relativistic general Kaluza-Klein space. This is done by using the Riemannian horizontal connection defined in [3], and some 4D horizontal tensor fields, as for instance: horizontal Ricci tensor, horizontal Einstein gravitational tensor field, horizontal electromagnetic energy-momentum tensor field, etc. Also, we present some inter-relations between STM theory and brane-world theory. This enables us to introduce in brane theory some electromagnetic potentials constructed by means of the warp function.
Renormalization group evolution of the universal theories EFT
NASA Astrophysics Data System (ADS)
Wells, James D.; Zhang, Zhengkang
2016-06-01
The conventional oblique parameters analyses of precision electroweak data can be consistently cast in the modern framework of the Standard Model effective field theory (SMEFT) when restrictions are imposed on the SMEFT parameter space so that it describes universal theories. However, the usefulness of such analyses is challenged by the fact that universal theories at the scale of new physics, where they are matched onto the SMEFT, can flow to nonuniversal theories with renormalization group (RG) evolution down to the electroweak scale, where precision observables are measured. The departure from universal theories at the electroweak scale is not arbitrary, but dictated by the universal parameters at the matching scale. But to define oblique parameters, and more generally universal parameters at the electroweak scale that directly map onto observables, additional prescriptions are needed for the treatment of RG-induced nonuniversal effects. We perform a RG analysis of the SMEFT description of universal theories, and discuss the impact of RG on simplified, universal-theories-motivated approaches to fitting precision electroweak and Higgs data.
Renormalization group evolution of the universal theories EFT
Wells, James D.; Zhang, Zhengkang
2016-06-21
The conventional oblique parameters analyses of precision electroweak data can be consistently cast in the modern framework of the Standard Model effective field theory (SMEFT) when restrictions are imposed on the SMEFT parameter space so that it describes universal theories. However, the usefulness of such analyses is challenged by the fact that universal theories at the scale of new physics, where they are matched onto the SMEFT, can flow to nonuniversal theories with renormalization group (RG) evolution down to the electroweak scale, where precision observables are measured. The departure from universal theories at the electroweak scale is not arbitrary, but dictated by the universal parameters at the matching scale. But to define oblique parameters, and more generally universal parameters at the electroweak scale that directly map onto observables, additional prescriptions are needed for the treatment of RG-induced nonuniversal effects. Finally, we perform a RG analysis of the SMEFT description of universal theories, and discuss the impact of RG on simplified, universal-theories-motivated approaches to fitting precision electroweak and Higgs data.
Renormalization group evolution of the universal theories EFT
Wells, James D.; Zhang, Zhengkang
2016-06-21
The conventional oblique parameters analyses of precision electroweak data can be consistently cast in the modern framework of the Standard Model effective field theory (SMEFT) when restrictions are imposed on the SMEFT parameter space so that it describes universal theories. However, the usefulness of such analyses is challenged by the fact that universal theories at the scale of new physics, where they are matched onto the SMEFT, can flow to nonuniversal theories with renormalization group (RG) evolution down to the electroweak scale, where precision observables are measured. The departure from universal theories at the electroweak scale is not arbitrary, butmore » dictated by the universal parameters at the matching scale. But to define oblique parameters, and more generally universal parameters at the electroweak scale that directly map onto observables, additional prescriptions are needed for the treatment of RG-induced nonuniversal effects. Finally, we perform a RG analysis of the SMEFT description of universal theories, and discuss the impact of RG on simplified, universal-theories-motivated approaches to fitting precision electroweak and Higgs data.« less
Introduction to conformal field theory and string theory
Dixon, L.J.
1989-12-01
These lectures are meant to provide a brief introduction to conformal field theory (CFT) and string theory for those with no prior exposure to the subjects. There are many excellent reviews already available, and most of these go in to much more detail than I will be able to here. 52 refs., 11 figs.
Group actions and anomalies in gauge theories
NASA Astrophysics Data System (ADS)
Catenacci, R.; Pirola, G. P.; Martellini, Maurizio; Reina, Cesare
1986-05-01
The transformation properties are studied of the vacuum functional W(A) for chiral fermions in a gauge potential A under the group A×U(1)×R+ of gauge, chiral and scale transformations. The vacuum functional W is identified with a section of a G×U(1)×R+ line bundle over the space A of all gauge potentials. Known results on bundles carrying group actions give a simple and unifying clue to non-abelian, abelian chiral anomalies, as well as to trace anomalies. While the first are due to the twisting of a line bundle on A/G, the abelian chiral and trace anomalies are related to characters of U(1) and R+ respectively. Characters of U(1) are basically controlled by ``winding numbers'', i.e. again by topology. Opposite to these, trace anomalies seem to have little to do with topology, with the exception of two-dimensional theories. Also at Gruppo Nazionale di Fisica Matematica, CNR.
Quantum Field Theory in Condensed Matter Physics
NASA Astrophysics Data System (ADS)
Tsvelik, Alexei M.
2007-01-01
Preface; Acknowledgements; Part I. Introduction to Methods: 1. QFT: language and goals; 2. Connection between quantum and classical: path integrals; 3. Definitions of correlation functions: Wick's theorem; 4. Free bosonic field in an external field; 5. Perturbation theory: Feynman diagrams; 6. Calculation methods for diagram series: divergences and their elimination; 7. Renormalization group procedures; 8. O(N)-symmetric vector model below the transition point; 9. Nonlinear sigma models in two dimensions: renormalization group and 1/N-expansion; 10. O(3) nonlinear sigma model in the strong coupling limit; Part II. Fermions: 11. Path integral and Wick's theorem for fermions; 12. Interaction electrons: the Fermi liquid; 13. Electrodynamics in metals; 14. Relativistic fermions: aspects of quantum electrodynamics; 15. Aharonov-Bohm effect and transmutation of statistics; Part III. Strongly Fluctuating Spin Systems: Introduction; 16. Schwinger-Wigner quantization procedure: nonlinear sigma models; 17. O(3) nonlinear sigma model in (2+1) dimensions: the phase diagram; 18. Order from disorder; 19. Jordan-Wigner transformations for spin S=1/2 models in D=1, 2, 3; 20. Majorana representation for spin S=1/2 magnets: relationship to Z2 lattice gauge theories; 21. Path integral representations for a doped antiferromagnet; Part IV. Physics in the World of One Spatial Dimension: Introduction; 22. Model of the free bosonic massless scalar field; 23. Relevant and irrelevant fields; 24. Kosterlitz-Thouless transition; 25. Conformal symmetry; 26. Virasoro algebra; 27. Differential equations for the correlation functions; 28. Ising model; 29. One-dimensional spinless fermions: Tomonaga-Luttinger liquid; 30. One-dimensional fermions with spin: spin-charge separation; 31. Kac-Moody algebras: Wess-Zumino-Novikov-Witten model; 32. Wess-Zumino-Novikov-Witten model in the Lagrangian form: non-Abelian bosonization; 33. Semiclassical approach to Wess-Zumino-Novikov-Witten models; 34
Fermion boson metamorphosis in field theory
Ha, Y.K.
1982-01-01
In two-dimensional field theories many features are especially transparent if the Fermi fields are represented by non-local expressions of the Bose fields. Such a procedure is known as boson representation. Bilinear quantities appear in the Lagrangian of a fermion theory transform, however, as simple local expressions of the bosons so that the resulting theory may be written as a theory of bosons. Conversely, a theory of bosons may be transformed into an equivalent theory of fermions. Together they provide a basis for generating many interesting equivalences between theories of different types. In the present work a consistent scheme for constructing a canonical Fermi field in terms of a real scalar field is developed and such a procedure is valid and consistent with the tenets of quantum field theory is verified. A boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. The nature of dynamical generation of mass when the theory undergoes boson transmutation and the preservation of continuous chiral symmetry in the massive case are examined. The dynamics of the system depends to a great extent on the specific number of fermions and different models of the same system can have very different properties. Many unusual symmetries of the fermion theory, such as hidden symmetry, duality and triality symmetries, are only manifest in the boson formulation. The underlying connections between some models with U(N) internal symmetry and another class of fermion models built with Majorana fermions which have O(2N) internal symmetry are uncovered.
Flat holography: aspects of the dual field theory
NASA Astrophysics Data System (ADS)
Bagchi, Arjun; Basu, Rudranil; Kakkar, Ashish; Mehra, Aditya
2016-12-01
Assuming the existence of a field theory in D dimensions dual to ( D + 1)-dimensional flat space, governed by the asymptotic symmetries of flat space, we make some preliminary remarks about the properties of this field theory. We review briefly some successes of the 3d bulk - 2d boundary case and then focus on the 4d bulk - 3d boundary example, where the symmetry in question is the infinite dimensional BMS4 algebra. We look at the constraints imposed by this symmetry on a 3d field theory by constructing highest weight representations of this algebra. We construct two and three point functions of BMS primary fields and surprisingly find that symmetries constrain these correlators to be identical to those of a 2d relativistic conformal field theory. We then go one dimension higher and construct prototypical examples of 4d field theories which are putative duals of 5d Minkowski spacetimes. These field theories are ultra-relativistic limits of electrodynamics and Yang-Mills theories which exhibit invariance under the conformal Carroll group in D = 4. We explore the different sectors within these Carrollian gauge theories and investigate the symmetries of the equations of motion to find that an infinite ultra-relativistic conformal structure arises in each case.
The affine structure of gravitational theories: Symplectic groups and geometry
NASA Astrophysics Data System (ADS)
Capozziello, Salvatore; Cirilo-Lombardo, D. J.; de Laurentis, Mariafelicia
2014-09-01
We give a geometrical description of gravitational theories from the viewpoint of symmetries and affine structure. We show how gravity, considered as a gauge theory, can be consistently achieved by the nonlinear realization of the conformal-affine group in an indirect manner: due to the partial isomorphism between CA(3, 1) and the centrally extended Sp( 8), we perform a nonlinear realization of the centrally extended (CE)Sp( 8) in its semi-simple version. In particular, starting from the bundle structure of gravity, we derive the conformal-affine Lie algebra and then, by the nonlinear realization, we define the coset field transformations, the Cartan forms and the inverse Higgs constraints. Finally, we discuss the geometrical Lagrangians where all the information on matter fields and their interactions can be contained.
Ostrogradsky in theories with multiple fields
Rham, Claudia de; Matas, Andrew
2016-06-23
We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamical or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.
Ostrogradsky in theories with multiple fields
NASA Astrophysics Data System (ADS)
de Rham, Claudia; Matas, Andrew
2016-06-01
We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamical or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.
Quantum cellular automata and free quantum field theory
NASA Astrophysics Data System (ADS)
D'Ariano, Giacomo Mauro; Perinotti, Paolo
2017-02-01
In a series of recent papers [1-4] it has been shown how free quantum field theory can be derived without using mechanical primitives (including space-time, special relativity, quantization rules, etc.), but only considering the easiest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the simple principles of unitarity, homogeneity, locality, and isotropy. This has opened the route to extending the axiomatic information-theoretic derivation of the quantum theory of abstract systems [5, 6] to include quantum field theory. The inherent discrete nature of the informational axiomatization leads to an extension of quantum field theory to a quantum cellular automata theory, where the usual field theory is recovered in a regime where the discrete structure of the automata cannot be probed. A simple heuristic argument sets the scale of discreteness to the Planck scale, and the customary physical regime where discreteness is not visible is the relativistic one of small wavevectors. In this paper we provide a thorough derivation from principles that in the most general case the graph of the quantum cellular automaton is the Cayley graph of a finitely presented group, and showing how for the case corresponding to Euclidean emergent space (where the group resorts to an Abelian one) the automata leads to Weyl, Dirac and Maxwell field dynamics in the relativistic limit. We conclude with some perspectives towards the more general scenario of non-linear automata for interacting quantum field theory.
3D quantum gravity and effective noncommutative quantum field theory.
Freidel, Laurent; Livine, Etera R
2006-06-09
We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.
A New Theory of the Electromagnetic Field
NASA Astrophysics Data System (ADS)
Kriske, Richard
2017-01-01
This author has previously introduced a new theory of the Electromagnetic Field and its interaction with matter. There was from the start a problem with Einstein's formulation of Invariants and its use in describing The EM field. The photon produced by first varying a stationary Electric field in one observer's reference frame is not the same as a photon produced from varying the a stationary Magnetic Field. The Magnetic field photon is thought of as being ``off the mass shell''. The Quantum information seems to carry with it an ordering of these events. You see this ordering in Wick's theory and in Feynman diagrams. This author is proposing that other fields can vary first in another Observers reference frame, not just the ``Scalar Field'' or the ``Fermion Field'', but many other forms of Energy. If the ``Nuclear Field'' varies first, it results in Quantum information that produces a photon that has the Nuclear Field in it and also the Magnetic Field, this is the strange effect seen in Nuclear Magnetic Resonance. This author proposed that there is a large number of photons with different properties, because of this ordering of events that occurs in Quantum Information. One of these photons is the Neutrino which appears to be a three field photon. This is Kriske's Field Theory.
Pure field theories and MACSYMA algorithms
NASA Technical Reports Server (NTRS)
Ament, W. S.
1977-01-01
A pure field theory attempts to describe physical phenomena through singularity-free solutions of field equations resulting from an action principle. The physics goes into forming the action principle and interpreting specific results. Algorithms for the intervening mathematical steps are sketched. Vacuum general relativity is a pure field theory, serving as model and providing checks for generalizations. The fields of general relativity are the 10 components of a symmetric Riemannian metric tensor; those of the Einstein-Straus generalization are the 16 components of a nonsymmetric. Algebraic properties are exploited in top level MACSYMA commands toward performing some of the algorithms of that generalization. The light cone for the theory as left by Einstein and Straus is found and simplifications of that theory are discussed.
An action for F-theory: {SL}(2){{{R}}}^{+} exceptional field theory
NASA Astrophysics Data System (ADS)
Berman, David S.; Blair, Chris D. A.; Malek, Emanuel; Rudolph, Felix J.
2016-10-01
We construct the 12-dimensional exceptional field theory (EFT) associated to the group {SL}(2)× {{{R}}}+. Demanding the closure of the algebra of local symmetries leads to a constraint, known as the section condition, that must be imposed on all fields. This constraint has two inequivalent solutions, one giving rise to 11-dimensional supergravity and the other leading to F-theory. Thus {SL}(2)× {{{R}}}+ EFT contains both F-theory and M-theory in a single 12-dimensional formalism.
Pion masses in quasiconformal gauge field theories
Dietrich, Dennis D.; Jaervinen, Matti
2009-03-01
We study modifications to Weinberg-like sum rules in quasiconformal gauge field theories. Beyond the two Weinberg sum rules and the oblique S parameter, we study the pion mass and the X parameter. Especially, we evaluate the pion mass for walking technicolor theories, in particular, minimal walking technicolor, and find contributions of the order of up to several hundred GeV.
Geometric continuum regularization of quantum field theory
Halpern, M.B. . Dept. of Physics)
1989-11-08
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.
{N}=3 four dimensional field theories
NASA Astrophysics Data System (ADS)
García-Etxebarria, Iñaki; Regalado, Diego
2016-03-01
We introduce a class of four dimensional field theories constructed by quotienting ordinary {N}=4 U(N ) SYM by particular combinations of R-symmetry and SL(2, ℤ) automorphisms. These theories appear naturally on the worldvolume of D3 branes probing terminal singularities in F-theory, where they can be thought of as non-perturbative generalizations of the O3 plane. We focus on cases preserving only 12 supercharges, where the quotient gives rise to theories with coupling fixed at a value of order one. These constructions possess an unconventional large N limit described by a non-trivial F-theory fibration with base AdS 5 × (S 5/ ℤ k ). Upon reduction on a circle the {N}=3 theories flow to well-known {N}=6 ABJM theories.
The Local Group: the ultimate deep field
NASA Astrophysics Data System (ADS)
Boylan-Kolchin, Michael; Weisz, Daniel R.; Bullock, James S.; Cooper, Michael C.
2016-10-01
Near-field cosmology - using detailed observations of the Local Group and its environs to study wide-ranging questions in galaxy formation and dark matter physics - has become a mature and rich field over the past decade. There are lingering concerns, however, that the relatively small size of the present-day Local Group (˜2 Mpc diameter) imposes insurmountable sample-variance uncertainties, limiting its broader utility. We consider the region spanned by the Local Group's progenitors at earlier times and show that it reaches 3 arcmin ≈ 7 comoving Mpc in linear size (a volume of ≈350 Mpc3) at z = 7. This size at early cosmic epochs is large enough to be representative in terms of the matter density and counts of dark matter haloes with Mvir(z = 7) ≲ 2 × 109 M⊙. The Local Group's stellar fossil record traces the cosmic evolution of galaxies with 103 ≲ M⋆(z = 0)/M⊙ ≲ 109 (reaching M1500 > -9 at z ˜ 7) over a region that is comparable to or larger than the Hubble Ultra-Deep Field (HUDF) for the entire history of the Universe. In the JWST era, resolved stellar populations will probe regions larger than the HUDF and any deep JWST fields, further enhancing the value of near-field cosmology.
Holographic renormalization group and cosmology in theories with quasilocalized gravity
NASA Astrophysics Data System (ADS)
Csáki, Csaba; Erlich, Joshua; Hollowood, Timothy J.; Terning, John
2001-03-01
We study the long distance behavior of brane theories with quasilocalized gravity. The five-dimensional (5D) effective theory at large scales follows from a holographic renormalization group flow. As intuitively expected, the graviton is effectively four dimensional at intermediate scales and becomes five dimensional at large scales. However, in the holographic effective theory the essentially 4D radion dominates at long distances and gives rise to scalar antigravity. The holographic description shows that at large distances the Gregory-Rubakov-Sibiryakov (GRS) model is equivalent to the model recently proposed by Dvali, Gabadadze, and Porrati (DGP), where a tensionless brane is embedded into 5D Minkowski space, with an additional induced 4D Einstein-Hilbert term on the brane. In the holographic description the radion of the GRS model is automatically localized on the tensionless brane, and provides the ghostlike field necessary to cancel the extra graviton polarization of the DGP model. Thus, there is a holographic duality between these theories. This analysis provides physical insight into how the GRS model works at intermediate scales; in particular it sheds light on the size of the width of the graviton resonance, and also demonstrates how the holographic renormalization group can be used as a practical tool for calculations.
Far-field environment working group summary
Pearcy, E.C.; Cady, R.E.
1995-09-01
This article is a summary of the proceedings of a group discussion which took place at the Workshop on the Role of Natural Analogs in Geologic Disposal of High-Level Nuclear Waste in San Antonio, Texas on July 22-25, 1991. The working group concentrated on the subject of the potential impacts of underground disposal of high-level radioactive wastes on the far-field environment.
Quantum algorithms for quantum field theories.
Jordan, Stephen P; Lee, Keith S M; Preskill, John
2012-06-01
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm.
Magnetic Catalysis in Graphene Effective Field Theory
NASA Astrophysics Data System (ADS)
DeTar, Carleton; Winterowd, Christopher; Zafeiropoulos, Savvas
2016-12-01
We report on the first calculation of magnetic catalysis at zero temperature in a fully nonperturbative simulation of the graphene effective field theory. Using lattice gauge theory, a nonperturbative analysis of the theory of strongly interacting, massless, (2 +1 )-dimensional Dirac fermions in the presence of an external magnetic field is performed. We show that in the zero-temperature limit, a nonzero value for the chiral condensate is obtained which signals the spontaneous breaking of chiral symmetry. This result implies a nonzero value for the dynamical mass of the Dirac quasiparticle.
"Quantum Field Theory and QCD"
Jaffe, Arthur M.
2006-02-25
This grant partially funded a meeting, "QFT & QCD: Past, Present and Future" held at Harvard University, Cambridge, MA on March 18-19, 2005. The participants ranged from senior scientists (including at least 9 Nobel Prize winners, and 1 Fields medalist) to graduate students and undergraduates. There were several hundred persons in attendance at each lecture. The lectures ranged from superlative reviews of past progress, lists of important, unsolved questions, to provocative hypotheses for future discovery. The project generated a great deal of interest on the internet, raising awareness and interest in the open questions of theoretical physics.
The Theory of Quantized Fields. II
DOE R&D Accomplishments Database
Schwinger, J.
1951-01-01
The arguments leading to the formulation of the Action Principle for a general field are presented. In association with the complete reduction of all numerical matrices into symmetrical and anti-symmetrical parts, the general field is decomposed into two sets, which are identified with Bose-Einstein and Fermi-Dirac fields. The spin restriction on the two kinds of fields is inferred from the time reflection invariance requirement. The consistency of the theory is verified in terms of a criterion involving the various generators of infinitesimal transformations. Following a discussion of charged fields, the electromagnetic field is introduced to satisfy the postulate of general gauge invariance. As an aspect of the latter, it is recognized that the electromagnetic field and charged fields are not kinematically independent. After a discussion of the field-strength commutation relations, the independent dynamical variable of the electromagnetic field are exhibited in terms of a special gauge.
Hunton Group core workshop and field trip
Johnson, K.S.
1993-12-31
The Late Ordovician-Silurian-Devonian Hunton Group is a moderately thick sequence of shallow-marine carbonates deposited on the south edge of the North American craton. This rock unit is a major target for petroleum exploration and reservoir development in the southern Midcontinent. The workshop described here was held to display cores, outcrop samples, and other reservoir-characterization studies of the Hunton Group and equivalent strata throughout the region. A field trip was organized to complement the workshop by allowing examination of excellent outcrops of the Hunton Group of the Arbuckle Mountains.
New symbolic tools for differential geometry, gravitation, and field theory
NASA Astrophysics Data System (ADS)
Anderson, I. M.; Torre, C. G.
2012-01-01
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, spinor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in gravitation and field theory. The purpose of this paper is to describe some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors, algebraic classification of solutions of the Einstein equations, and symmetry reduction of field equations.
From theory to field experiments
NASA Astrophysics Data System (ADS)
de Vos, Bram
2016-04-01
Peter Raats' achievements in Haren (NL) 1986-1997 were based on a solid theoretical insight in hydrology and transport process in soil. However, Peter was also the driving force behind many experimental studies and applied research. This will be illustrated by a broad range of examples ranging from the dynamics of composting processes of organic material; modelling and monitoring nutrient leaching at field-scale; wind erosion; water and nutrient dynamics in horticultural production systems; oxygen diffusion in soils; and processes of water and nutrient uptake by plant roots. Peter's leadership led to may new approaches and the introduction of innovative measurement techniques in Dutch research; ranging from TDR to nutrient concentration measurements in closed fertigation systems. This presentation will give a brief overview how Peter's theoretical and mathematical insights accelerated this applied research.
Phase-space quantization of field theory.
Curtright, T.; Zachos, C.
1999-04-20
In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999.
Geomagnetic Field -- From Paleomagnetism to Dynamo Theory
NASA Astrophysics Data System (ADS)
Kono, M.
2008-05-01
Since 1995, self-consistent models of the geodynamo became available. There are certain problems, but some of these models have shown behaviors quite similar to those observed by paleomagnetism, including polarity reversals (Kono and Roberts, 2002). There is thus a hope that the combination of paleomagnetism and dynamo theory may provide us a very comprehensive understanding of the geomagnetic field. In this paper, I will try to highlight the possibilities and limitations in such studies. From satellite observations, it was shown that the power of the magnetic field contained in each degree is nearly the same if measured at the core-mantle boundary (CMB). The core field can be seen only to degree 13 or 14 where the field power is about (10 nT)2. Beyond that, the crustal magnetization dominates and the core signal is lost. The value of 10 nT is far larger than the accuracy of the present-day instruments, but much smaller than the resolution obtainable by paleomagnetic observations. We may safely assume that the error in paleomagnetic measurements (in direction) is of the order of 10 degrees. This error corresponds to the resolution of about 1/5. The relative powers of the low degree terms in the magnetic field at the surface are 1.0, 0.033, 0.019, 0.0055 (Langel and Estes, 1982). This means that only the degrees 1 to 3 terms may be distinguished by paleomagnetic data. From the combination of dipole, quadrupole, and octupole, what we can deduce about the fundamental properties of the geomagnetic field? Here are some of the possibilities, which may give important clues when we compare with dynamo simulation results. (1) The current dipole power is several times larger than the value expected from the trend line produced by degrees 2--13. Is this a persistent feature or transient? (2) In PSV analysis, the angular standard deviation increases with latitude. Kono and Tanaka (1995) showed that it is possible only if the (2,1) (degree, order) or (3,2) term is very large
Protected gates for topological quantum field theories
NASA Astrophysics Data System (ADS)
Beverland, Michael E.; Buerschaper, Oliver; Koenig, Robert; Pastawski, Fernando; Preskill, John; Sijher, Sumit
2016-02-01
We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators — for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons, in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.
Protected gates for topological quantum field theories
Beverland, Michael E.; Pastawski, Fernando; Preskill, John; Buerschaper, Oliver; Koenig, Robert; Sijher, Sumit
2016-02-15
We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators — for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons, in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.
Bound states in gauge theories as the Poincare group representations
Cherny, A. Yu.; Dorokhov, A. E.; Han, Nguyen Suan; Pervushin, V. N. Shilin, V. I.
2013-03-15
The bound-state generating functional is constructed in gauge theories. This construction is based on the Dirac Hamiltonian approach to gauge theories, the Poincare group classification of fields and their nonlocal bound states, and the Markov-Yukawa constraint of irreducibility. The generating functional contains additional anomalous creations of pseudoscalar bound states: para-positronium in QED and mesons inQCDin the two-gamma processes of the type of {gamma} + {gamma} {yields} {pi}{sub 0} +para-positronium. The functional allows us to establish physically clear and transparent relations between the perturbativeQCD to its nonperturbative low-energy model by means of normal ordering and the quark and gluon condensates. In the limit of small current quark masses, the Gell-Mann-Oakes-Renner relation is derived from the Schwinger-Dyson and Bethe-Salpeter equations. The constituent quark masses can be calculated from a self-consistent nonlinear equation.
Free Quantum Field Theory from Quantum Cellular Automata
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro
2015-10-01
After leading to a new axiomatic derivation of quantum theory (see D'Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).
Small Group Learning: Do Group Members' Implicit Theories of Ability Make a Difference?
ERIC Educational Resources Information Center
Beckmann, Nadin; Wood, Robert E.; Minbashian, Amirali; Tabernero, Carmen
2012-01-01
We examined the impact of members' implicit theories of ability on group learning and the mediating role of several group process variables, such as goal-setting, effort attributions, and efficacy beliefs. Comparisons were between 15 groups with a strong incremental view on ability (high incremental theory groups), and 15 groups with a weak…
Working group on chromospheric fields - Canopies
NASA Technical Reports Server (NTRS)
Jones, H. P.
1985-01-01
Although there are many points of uncertainty and controversy, the working group on chromospheric fields focussed its discussion on the concept of canopies; i.e., no one disagreed that a central issue relating to magnetic fields and chromospheric models is to learn how the photospheric field spreads with height. However, it quickly became apparent that in the time available, there was little prospect of building new unified models of magnetic field phenomena in the chromosphere beyond the scope of the formal presentations. Thus, the discussion was devoted to formulating questions which seemed both possible to address in future work and important for advancing understanding of the chromosphere. It began by discussing unresolved physical issues (almost everything) and then proceeded to consider means, both observational and synthetic, to address them.
Cutkosky rules for superstring field theory
NASA Astrophysics Data System (ADS)
Pius, Roji; Sen, Ashoke
2016-10-01
Superstring field theory expresses the perturbative S-matrix of superstring theory as a sum of Feynman diagrams each of which is manifestly free from ultraviolet divergences. The interaction vertices fall off exponentially for large space-like external momenta making the ultraviolet finiteness property manifest, but blow up exponentially for large time-like external momenta making it impossible to take the integration contours for loop energies to lie along the real axis. This forces us to carry out the integrals over the loop energies by choosing appropriate contours in the complex plane whose ends go to infinity along the imaginary axis but which take complicated form in the interior navigating around the various poles of the propagators. We consider the general class of quantum field theories with this property and prove Cutkosky rules for the amplitudes to all orders in perturbation theory. Besides having applications to string field theory, these results also give an alternative derivation of Cutkosky rules in ordinary quantum field theories.
Weak gravity conjecture and effective field theory
NASA Astrophysics Data System (ADS)
Saraswat, Prashant
2017-01-01
The weak gravity conjecture (WGC) is a proposed constraint on theories with gauge fields and gravity, requiring the existence of light charged particles and/or imposing an upper bound on the field theory cutoff Λ . If taken as a consistency requirement for effective field theories (EFTs), it rules out possibilities for model building including some models of inflation. I demonstrate simple models which satisfy all forms of the WGC, but which through Higgsing of the original gauge fields produce low-energy EFTs with gauge forces that badly violate the WGC. These models illustrate specific loopholes in arguments that motivate the WGC from a bottom-up perspective; for example the arguments based on magnetic monopoles are evaded when the magnetic confinement that occurs in a Higgs phase is accounted for. This indicates that the WGC should not be taken as a veto on EFTs, even if it turns out to be a robust property of UV quantum gravity theories. However, if the latter is true, then parametric violation of the WGC at low energy comes at the cost of nonminimal field content in the UV. I propose that only a very weak constraint is applicable to EFTs, Λ ≲(log 1/g )-1 /2Mpl , where g is the gauge coupling, motivated by entropy bounds. Remarkably, EFTs produced by Higgsing a theory that satisfies the WGC can saturate but not violate this bound.
On space of integrable quantum field theories
NASA Astrophysics Data System (ADS)
Smirnov, F. A.; Zamolodchikov, A. B.
2017-02-01
We study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as "effective field theories", with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields Xs, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars Xs are built from the components of the associated conserved currents in a universal way. The first of these scalars, X1, coincides with the composite field (T T bar) built from the components of the energy-momentum tensor. The deformations of quantum field theories generated by X1 are "solvable" in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations Xs are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit construction of the form factors of the operators Xs in sine-Gordon theory. We also make some remarks on the problem of UV completeness of such integrable deformations.
Field theories without a holographic dual
NASA Astrophysics Data System (ADS)
McInnes, Brett
2016-12-01
In applying the gauge-gravity duality to the quark-gluon plasma, one models the plasma using a particular kind of field theory with specified values of the temperature, magnetic field, and so forth. One then assumes that the bulk, an asymptotically AdS black hole spacetime with properties chosen to match those of the boundary field theory, can be embedded in string theory. But this is not always the case: there are field theories with no bulk dual. The question is whether these theories might include those used to study the actual plasmas produced at such facilities as the RHIC experiment or the relevant experiments at the LHC. We argue that, provided that due care is taken to include the effects of the angular momentum associated with the magnetic fields experienced by the plasmas produced by peripheral collisions, the existence of the dual can be established for the RHIC plasmas. In the case of the LHC plasmas, the situation is much more doubtful.
Nonequilibrium statistical field theory for classical particles: Basic kinetic theory.
Viermann, Celia; Fabis, Felix; Kozlikin, Elena; Lilow, Robert; Bartelmann, Matthias
2015-06-01
Recently Mazenko and Das and Mazenko [Phys. Rev. E 81, 061102 (2010); J. Stat. Phys. 149, 643 (2012); J. Stat. Phys. 152, 159 (2013); Phys. Rev. E 83, 041125 (2011)] introduced a nonequilibrium field-theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual particle. We use this theory to investigate the transition from those microscopic degrees of freedom to the evolution equations of the macroscopic observables of the ensemble. For the free theory, we recover the continuity and Jeans equations of a collisionless gas. For a theory containing two-particle interactions in a canonical perturbation series, we find the macroscopic evolution equations to be described by the Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy with a truncation criterion depending on the order in perturbation theory. This establishes a direct link between the classical and the field-theoretical approaches to kinetic theory that might serve as a starting point to investigate kinetic theory beyond the classical limits.
Interacting scale invariant but nonconformal field theories
NASA Astrophysics Data System (ADS)
Nakayama, Yu
2017-03-01
There is a dilemma in constructing interacting scale invariant Euclidean field theories that are not conformal invariant. On one hand, scale invariance without conformal invariance seems more generic by requiring only a smaller symmetry. On the other hand, the existence of a nonconserved current with exact scaling dimension d -1 in d dimensions seems to require extra fine-tuning. To understand the competition better, we explore some examples without the reflection positivity. We show that a theory of elasticity (also known as Riva-Cardy theory) coupled with massless fermions in d =4 -ɛ dimensions does not possess an interacting scale invariant fixed point except for an unstable (and unphysical) one with an infinite coefficient of compression. We do, however, find interacting scale invariant but nonconformal field theories in gauge fixed versions of the Banks-Zaks fixed points in d =4 dimensions.
Field Theory for Multi-Particle System
NASA Astrophysics Data System (ADS)
Wang, Shouhong; Ma, Tian
2016-03-01
The main objectives of this talk are 1) to introduce some basic postulates for quantum multi-particle systems, and 2) to develop a universal field theory for interacting multi-particle systems coupling both particle fields and interacting fields. By carefully examining the nature of interactions between multi-particles, we conclude that multi-particle systems must obey i) the gauge symmetry, ii) the principle of interaction dynamics (PID), and iii) the principle of representation invariance (PRI). Intuitively, PID takes the variation of the action functional under energy-momentum conservation constraint, offers a different and natural way of introducing Higgs fields, and is also required by the presence of dark matter and dark energy and the quark confinement. PRI requires that the SU(N) gauge theory be independent of representations of SU(N). Based on these principles, a few basic postulates for multi-particle systems are introduced in this talk, leading to a field theory for interacting multi-particle systems. A direct consequence of the field theory is the derivation of general atomic spectrum equations. Supported in Part by the Office of Naval Research, by the US National Science Foundation, and by the Chinese National Science Foundation.
Dynamical theory of dense groups of galaxies
NASA Technical Reports Server (NTRS)
Mamon, Gary A.
1990-01-01
It is well known that galaxies associate in groups and clusters. Perhaps 40% of all galaxies are found in groups of 4 to 20 galaxies (e.g., Tully 1987). Although most groups appear to be so loose that the galaxy interactions within them ought to be insignificant, the apparently densest groups, known as compact groups appear so dense when seen in projection onto the plane of the sky that their members often overlap. These groups thus appear as dense as the cores of rich clusters. The most popular catalog of compact groups, compiled by Hickson (1982), includes isolation among its selection critera. Therefore, in comparison with the cores of rich clusters, Hickson's compact groups (HCGs) appear to be the densest isolated regions in the Universe (in galaxies per unit volume), and thus provide in principle a clean laboratory for studying the competition of very strong gravitational interactions. The $64,000 question here is then: Are compact groups really bound systems as dense as they appear? If dense groups indeed exist, then one expects that each of the dynamical processes leading to the interaction of their member galaxies should be greatly enhanced. This leads us to the questions: How stable are dense groups? How do they form? And the related question, fascinating to any theorist: What dynamical processes predominate in dense groups of galaxies? If HCGs are not bound dense systems, but instead 1D change alignments (Mamon 1986, 1987; Walke & Mamon 1989) or 3D transient cores (Rose 1979) within larger looser systems of galaxies, then the relevant question is: How frequent are chance configurations within loose groups? Here, the author answers these last four questions after comparing in some detail the methods used and the results obtained in the different studies of dense groups.
Symmetry, Group Theory, and the Physical Properties of Crystals
NASA Astrophysics Data System (ADS)
Powell, Richard C.
The intent of this book is to demonstrate the importance of symmetry in determining the properties of solids and the power of using group theory and tensor algebra to elucidate these properties. It is not meant to be a comprehensive text on solid state physics, so many important aspects of condensed matter physics not related to symmetry are not covered here. The book begins by discussing the concepts of symmetry relevant to crystal structures. This is followed by a summary of the basics of group theory and how it is applied to quantum mechanics. Next is a discussion of the description of the macroscopic properties of crystals by tensors and how symmetry determines the form of these tensors. The basic concepts covered in these early chapters are then applied to a series of different examples. There is a discussion of the use of point symmetry in the crystal field theory treatment of point defects in solids. Next is a discussion of crystal symmetry in determining the optical properties of solids, followed by a chapter on the nonlinear optical properties of solids. Then the role of symmetry in treating lattice vibrations is described. The last chapter discusses the effects of translational symmetry on electronic energy bands in solids.
Quantum field theory of treasury bonds.
Baaquie, B E
2001-07-01
The Heath-Jarrow-Morton (HJM) formulation of treasury bonds in terms of forward rates is recast as a problem in path integration. The HJM model is generalized to the case where all the forward rates are allowed to fluctuate independently. The resulting theory is shown to be a two-dimensional Gaussian quantum field theory. The no arbitrage condition is obtained and a functional integral derivation is given for the price of a futures and an options contract.
Magnetic monopoles in field theory and cosmology.
Rajantie, Arttu
2012-12-28
The existence of magnetic monopoles is predicted by many theories of particle physics beyond the standard model. However, in spite of extensive searches, there is no experimental or observational sign of them. I review the role of magnetic monopoles in quantum field theory and discuss their implications for particle physics and cosmology. I also highlight their differences and similarities with monopoles found in frustrated magnetic systems.
Recursive renormalization group theory based subgrid modeling
NASA Technical Reports Server (NTRS)
Zhou, YE
1991-01-01
Advancing the knowledge and understanding of turbulence theory is addressed. Specific problems to be addressed will include studies of subgrid models to understand the effects of unresolved small scale dynamics on the large scale motion which, if successful, might substantially reduce the number of degrees of freedom that need to be computed in turbulence simulation.
Localization and Dualities in Three-dimensional Superconformal Field Theories
NASA Astrophysics Data System (ADS)
Willett, Brian
In this thesis we apply the technique of localization to three-dimensional N = 2 superconformal field theories. We consider both theories which are exactly superconformal, and those which are believed to flow to nontrivial superconformal fixed points, for which we consider implicitly these fixed points. We find that in such theories, the partition function and certain supersymmetric observables, such as Wilson loops, can be computed exactly by a matrix model. This matrix model consists of an integral over g , the Lie algebra of the gauge group of the theory, of a certain product of 1-loop factors and classical contributions. One can also consider a space of supersymmetric deformations of the partition function corresponding to the set of abelian global symmetries. In the second part of the thesis we apply these results to test dualities. We start with the case of ABJM theory, which is dual to M-theory on an asymptotically AdS4 x S7 background. We extract strong coupling results in the field theory, which can be compared to semiclassical, weak coupling results in the gravity theory, and a nontrivial agreement is found. We also consider several classes of dualities between two three-dimensional field theories, namely, 3D mirror symmetry, Aharony duality, and Giveon-Kutasov duality. Here the dualities are typically between the IR limits of two Yang-Mills theories, which are strongly coupled in three dimensions since Yang-Mills theory is asymptotically free here. Thus the comparison is again very nontrivial, and relies on the exactness of the localization computation. We also compare the deformed partition functions, which tests the mapping of global symmetries of the dual theories. Finally, we discuss some recent progress in the understanding of general three-dimensional theories in the form of the F-theorem, a conjectured analogy to the a-theorem in four dimensions and c-theorem in two dimensions, which is closely related to the localization computation.
Diagrammar in classical scalar field theory
Cattaruzza, E.; Gozzi, E.; Francisco Neto, A.
2011-09-15
In this paper we analyze perturbatively a g{phi}{sup 4}classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that a universal supersymmetry present in the classical path-integral mentioned above is responsible for the cancelation of various diagrams. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplify the calculations and make the classical perturbative calculations almost 'identical' formally to the quantum ones. Using the super-diagrams technique, we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem. - Highlights: > We provide the Feynman diagrams of perturbation theory for a classical field theory. > We give a super-formalism which links the quantum diagrams to the classical ones. > We check perturbatively the fluctuation-dissipation theorem.
Group theory and dynamics of neutrino mixing
NASA Astrophysics Data System (ADS)
Lam, C. S.
2011-06-01
There is a direct group-theoretical connection between neutrino mixing and horizontal symmetry that can be established without any dynamical input. Such a connection is reviewed and expanded in this article. For certain symmetry groups G including A4 and S4, it is shown that a generic U(1)×G Higgs potential of a valon yields exactly the alignments dictated by the group-theoretical approach, but energy can now be used to discriminate different alignments. This mechanism possibly explains why starting from an A4 group, the tribimaximal mixing matrix with an enhanced S4 symmetry is more preferable than the one without it.
Chiral orbifold construction of field theories with extra dimensions
NASA Astrophysics Data System (ADS)
Hailu, Girma
We build higher dimensional field theories which have chiral fermion zero-modes on orbifolds. We show that orbifold boundary conditions and scalar vacuum expectation values interplay to produce chiral fermions localized on fat three branes. We develop a scheme for computing field propagators in higher dimensional theories obeying chiral orbifold boundary conditions. Using this scheme we compute the loop corrections to an effective field theory in five dimensions. We find that the renormalization group running of the higher dimensional bulk theory leads to a running of the four dimensional brane couplings. We generalize an argument to verify that the chiral anomaly that arises in these chiral orbifold theories is entirely confined on and uniformly distributed over the fixed points of the orbifold, independent of the shape of the chiral zero-modes. We construct a setup in which a scalar field with appropriate profile in the extra dimension is used to address the hierarchy problem and also localize both chiral fermions and zero-mode gravitons on the same three brane in five dimensions. We construct exact and nonpetrurbative quantum moduli spaces and dynamical superpotentials of an infinite set of linear and ring N = 1 supersymmetric moose theories with SU(2) gauge group at each node and link chiral superfields in the fundamental representation.
Effective field theory for deformed atomic nuclei
Papenbrock, Thomas F.; Weidenmüller, H. A.
2016-04-13
In this paper, we present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband E2 transitions. Finally, for rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
Arrival time in quantum field theory
NASA Astrophysics Data System (ADS)
Wang, Zhi-Yong; Xiong, Cai-Dong; He, Bing
2008-09-01
Via the proper-time eigenstates (event states) instead of the proper-mass eigenstates (particle states), free-motion time-of-arrival theory for massive spin-1/2 particles is developed at the level of quantum field theory. The approach is based on a position-momentum dual formalism. Within the framework of field quantization, the total time-of-arrival is the sum of the single event-of-arrival contributions, and contains zero-point quantum fluctuations because the clocks under consideration follow the laws of quantum mechanics.
Recent progress in irrational conformal field theory
Halpern, M.B.
1993-09-01
In this talk, I will review the foundations of irrational conformal field theory (ICFT), which includes rational conformal field theory as a small subspace. Highlights of the review include the Virasoro master equation, the Ward identities for the correlators of ICFT and solutions of the Ward identities. In particular, I will discuss the solutions for the correlators of the g/h coset construction and the correlators of the affine-Sugawara nests on g {contains} h{sub 1} {contains} {hor_ellipsis} {contains} h{sub n}. Finally, I will discuss the recent global solution for the correlators of all the ICFT`s in the master equation.
Effective field theory for deformed atomic nuclei
NASA Astrophysics Data System (ADS)
Papenbrock, T.; Weidenmüller, H. A.
2016-05-01
We present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband E2 transitions. For rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
A geometric formulation of exceptional field theory
NASA Astrophysics Data System (ADS)
du Bosque, Pascal; Hassler, Falk; Lüst, Dieter; Malek, Emanuel
2017-03-01
We formulate the full bosonic SL(5) exceptional field theory in a coordinateinvariant manner. Thereby we interpret the 10-dimensional extended space as a manifold with SL(5) × ℝ +-structure. We show that the algebra of generalised diffeomorphisms closes subject to a set of closure constraints which are reminiscent of the quadratic and linear constraints of maximal seven-dimensional gauged supergravities, as well as the section condition. We construct an action for the full bosonic SL(5) exceptional field theory, even when the SL(5) × ℝ +-structure is not locally flat.
Dual field theory of strong interactions
Akers, D.
1987-07-01
A dual field theory of strong interactions is derived from a Lagrangian of the Yang-Mills and Higgs fields. The existence of a magnetic monopole of mass 2397 MeV and Dirac charge g = (137/2)e is incorporated into the theory. Unification of the strong, weak, and electromagnetic forces is shown to converge at the mass of the intermediate vector boson W/sup +/-/. The coupling constants of the strong and weak interactions are derived in terms of the fine-structure constant ..cap alpha.. = 1/137.
The field theory of specific heat
NASA Astrophysics Data System (ADS)
Gusev, Yu. V.
2016-01-01
Finite temperature quantum field theory in the heat kernel method is used to study the heat capacity of condensed matter. The lattice heat is treated à la P. Debye as energy of the elastic (sound) waves. The dimensionless functional of free energy is re-derived with a cut-off parameter and used to obtain the specific heat of crystal lattices. The new dimensionless thermodynamical variable is formed as Planck's inverse temperature divided by the lattice constant. The dimensionless constant, universal for the class of crystal lattices, which determines the low temperature region of molar specific heat, is introduced and tested with the data for diamond lattice crystals. The low temperature asymptotics of specific heat is found to be the fourth power in temperature instead of the cubic power law of the Debye theory. Experimental data for the carbon group elements (silicon, germanium) and other materials decisively confirm the quartic law. The true low temperature regime of specific heat is defined by the surface heat, therefore, it depends on the geometrical characteristics of the body, while the absolute zero temperature limit is geometrically forbidden. The limit on the growth of specific heat at temperatures close to critical points, known as the Dulong-Petit law, appears from the lattice constant cut-off. Its value depends on the lattice type and it is the same for materials with the same crystal lattice. The Dulong-Petit values of compounds are equal to those of elements with the same crystal lattice type, if one mole of solid state matter were taken as the Avogadro number of the composing atoms. Thus, the Neumann-Kopp law is valid only in some special cases.
Long-range interactions in lattice field theory
Rabin, J.M.
1981-06-01
Lattice quantum field theories containing fermions can be formulated in a chirally invariant way provided long-range interactions are introduced. It is established that in weak-coupling perturbation theory such a lattice theory is renormalizable when the corresponding continuum theory is, and that the continuum theory is indeed recovered in the perturbative continuum limit. In the strong-coupling limit of these theories one is led to study an effective Hamiltonian describing a Heisenberg antiferromagnet with long-range interactions. Block-spin renormalization group methods are used to find a critical rate of falloff of the interactions, approximately as inverse distance squared, which separates a nearest-neighbor-antiferromagnetic phase from a phase displaying identifiable long-range effects. A duality-type symmetry is present in some block-spin calculations.
Near-field optical thin microcavity theory
NASA Astrophysics Data System (ADS)
Wu, Jiu Hui; Hou, Jiejie
2016-01-01
The thin microcavity theory for near-field optics is proposed in this study. By applying the power flow theorem and the variable theorem,the bi-harmonic differential governing equation for electromagnetic field of a three-dimensional thin microcavity is derived for the first time. Then by using the Hankel transform, this governing equation is solved exactly and all the electromagnetic components inside and outside the microcavity can be obtained accurately. According to the above theory, the near-field optical diffraction from a subwavelength aperture embedded in a thin conducting film is investigated, and numerical computations are performed to illustrate the edge effect by an enhancement factor of 1.8 and the depolarization phenomenon of the near-field transmission in terms of the distance from the film surface. This thin microcavity theory is verified by the good agreement between our results and those in the previous literatures. The thin microcavity theory presented in the study should be useful in the possible applications of the thin microcavities in near-field optics and thin-film optics.
Generalized conservation laws in non-local field theories
NASA Astrophysics Data System (ADS)
Kegeles, Alexander; Oriti, Daniele
2016-04-01
We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a generalized conservation law, in which the usual conserved current acquires an additional non-local correction term, obtaining a generalization of the standard Noether theorem. We illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of Bose-Einstein condensates. We expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity.
Natural discretization in noncommutative field theory
NASA Astrophysics Data System (ADS)
Acatrinei, Ciprian Sorin
2015-12-01
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Natural discretization in noncommutative field theory
Acatrinei, Ciprian Sorin
2015-12-07
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Astrophysical data analysis with information field theory
Enßlin, Torsten
2014-12-05
Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.
Gravitational radiative corrections from effective field theory
Goldberger, Walter D.; Ross, Andreas
2010-06-15
In this paper we construct an effective field theory (EFT) that describes long wavelength gravitational radiation from compact systems. To leading order, this EFT consists of the multipole expansion, which we describe in terms of a diffeomorphism invariant point particle Lagrangian. The EFT also systematically captures 'post-Minkowskian' corrections to the multipole expansion due to nonlinear terms in general relativity. Specifically, we compute long distance corrections from the coupling of the (mass) monopole moment to the quadrupole moment, including up to two mass insertions. Along the way, we encounter both logarithmic short distance (UV) and long wavelength (IR) divergences. We show that the UV divergences can be (1) absorbed into a renormalization of the multipole moments and (2) resummed via the renormalization group. The IR singularities are shown to cancel from properly defined physical observables. As a concrete example of the formalism, we use this EFT to reproduce a number of post-Newtonian corrections to the gravitational wave energy flux from nonrelativistic binaries, including long distance effects up to 3 post-Newtonian (v{sup 6}) order. Our results verify that the factorization of scales proposed in the NRGR framework of Goldberger and Rothstein is consistent up to order 3PN.
Symmetry analysis for anisotropic field theories
Parra, Lorena; Vergara, J. David
2012-08-24
The purpose of this paper is to study with the help of Noether's theorem the symmetries of anisotropic actions for arbitrary fields which generally depend on higher order spatial derivatives, and to find the corresponding current densities and the Noether charges. We study in particular scale invariance and consider the cases of higher derivative extensions of the scalar field, electrodynamics and Chern-Simons theory.
Generating Quasigroups: A Group Theory Investigation
ERIC Educational Resources Information Center
Lynch, Mark A. M.
2011-01-01
A procedure for generating quasigroups from groups is described, and the properties of these derived quasigroups are investigated. Some practical examples of the procedure and related results are presented.
Not Available
1992-01-01
The effort of the experimental group has been concentrated on the CERN ALEPH and FERMILAB D0 collider experiments and completion of two fixed target experiments. The BNL fixed target experiment 771 took the world's largest sample of D(1285) and E/iota(1420) events, using pion, kaon and antiproton beams. Observing the following resonances: 0[sup [minus plus
Mean Field Theories of Icosahedral Quasicrystals.
NASA Astrophysics Data System (ADS)
Troian, Sandra Marina
In 1984 Shechtman et al. discovered a metallic solid (Al(,86)Mn(,14)) with diffraction spots as sharp as those of crystals but with icosahedral point group symmetry, known to be incompatible with translational symmetry. One of the interesting crystallographic questions posed by the discovery of quasicrystals, as these materials are now called, is why does the atomic density assume an icosahedrally symmetric configuration in preference to conventional periodic crystalline forms. To address this question, we use a phenomenological approach based on the Landau theory of crystal formation (Landau, 1937) to ascertain whether any of the conventional elementary approaches to crystal formation might not contain metastable (or even stable) quasicrystalline solutions hitherto overlooked because of the almost universal prejudice that positional ordering must be periodic. Alexander and McTague (1978) touched on the possibility of icosahedrally symmetric structures using a (single order parameter) Landau free energy. We reexamine and extend their model and find that there are three distinct icosahedral stationary points to the free energy, although none of them is ever globally stable compared with more conventional competing structures like the body-centered cubic, hexagonal, or smectic. Which periodic form is favored depends on the temperature range investigated. We find that two of these stationary points are not even local minima of the free energy. We generalize this model by constructing a Landau theory for two or three-component systems, which appear to give a region of the phase diagram in which icosahedral quasicrystalline ordering is the state of lowest free energy. The quasicrystals are stabilized by special geometric ratios between the length scales characterizing the components. Three components are required to stabilize a two-dimensional quasicrystal but two components suffice to stabilize a three-dimensional one. We present results for two different ratios
Causality constraints in conformal field theory
Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
2016-05-17
Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well known sign constraint on the (Φ)^{4} coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. As a result, our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators
Causality constraints in conformal field theory
NASA Astrophysics Data System (ADS)
Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
2016-05-01
Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well known sign constraint on the (∂ ϕ)4 coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. Our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators.
Mean-field kinetic nucleation theory
NASA Astrophysics Data System (ADS)
Kalikmanov, V. I.
2006-03-01
A new semiphenomenological model of homogeneous vapor-liquid nucleation is proposed in which the cluster kinetics follows the "kinetic approach to nucleation" and the thermodynamic part is based on the revised Fisher droplet model with the mean-field argument for the cluster configuration integral. The theory is nonperturbative in a cluster size and as such is valid for all clusters down to monomers. It contains two surface tensions: macroscopic (planar) and microscopic. The latter is a temperature dependent quantity related to the vapor compressibility factor at saturation. For Lennard-Jones fluids the microscopic surface tension possesses a universal behavior with the parameters found from the mean-field density functional calculations. The theory is verified against nucleation experiments for argon, nitrogen, water, and mercury, demonstrating very good agreement with experimental data. Classical nucleation theory fails to predict experimental results when a critical cluster becomes small.
Cross Sections From Scalar Field Theory
NASA Technical Reports Server (NTRS)
Norbury, John W.; Dick, Frank; Norman, Ryan B.; Nasto, Rachel
2008-01-01
A one pion exchange scalar model is used to calculate differential and total cross sections for pion production through nucleon- nucleon collisions. The collisions involve intermediate delta particle production and decay to nucleons and a pion. The model provides the basic theoretical framework for scalar field theory and can be applied to particle production processes where the effects of spin can be neglected.
An Introduction to Effective Field Theory
NASA Astrophysics Data System (ADS)
Burgess, C. P.
2007-11-01
This review summarizes effective field theory techniques, which are the modern theoretical tools for exploiting the existence of hierarchies of scale in a physical problem. The general theoretical framework is described and evaluated explicitly for a simple model. Power-counting results are illustrated for a few cases of practical interest, and several applications to quantum electrodynamics are described.
Effective Field Theories of Nuclear Structure
NASA Astrophysics Data System (ADS)
Furnstahl, Richard
1996-10-01
Traditional nuclear structure calculations have been pushed to new heights recently by exploiting new methods and increased computational power.(B. Pudliner et al)., Phys. Rev. Lett. 74, 4396 (1995); S.E. Koonin et al., nucl-th/9602006 (1996). Nevertheless, these developments have been made without direct input from quantum chromodynamics (QCD), the basic theory of strong interactions. Effective Field Theory provides a framework for connecting the energy scales and degrees of freedom appropriate for nuclear structure with those in the underlying QCD. Recent work shows how spontaneously broken chiral symmetry constrains the systematics of few-body nuclei.(See, for example, J.L. Friar, Few-Body Systems Suppl. 99), 1 (1996). Important ingredients are dimensional power counting and the assumption of naturalness,(A. Manohar and H. Georgi, Nucl. Phys. B234), 189 (1984). which allow estimates of the sizes of terms in effective lagrangians and imply the hierarchy of nuclear many-body forces. The delicacies of nuclear saturation introduce formidable obstacles to the systematic extension of effective chiral field theory to finite densities. For heavier nuclei, however, the successes of relativistic mean-field phenomenology can be understood in terms of nonrenormalizable effective field theories that are consistent with the symmetries of QCD. This framework provides new insight into issues of relativistic versus nonrelativistic formulations, nucleon compositeness, vacuum contributions, and extrapolations to high density.
Perturbative quantum gravity in double field theory
NASA Astrophysics Data System (ADS)
Boels, Rutger H.; Horst, Christoph
2016-04-01
We study perturbative general relativity with a two-form and a dilaton using the double field theory formulation which features explicit index factorisation at the Lagrangian level. Explicit checks to known tree level results are performed. In a natural covariant gauge a ghost-like scalar which contributes even at tree level is shown to decouple consistently as required by perturbative unitarity. In addition, a lightcone gauge is explored which bypasses the problem altogether. Using this gauge to study BCFW on-shell recursion, we can show that most of the D-dimensional tree level S-matrix of the theory, including all pure graviton scattering amplitudes, is reproduced by the double field theory. More generally, we argue that the integrand may be reconstructed from its single cuts and provide limited evidence for off-shell cancellations in the Feynman graphs. As a straightforward application of the developed technology double field theory-like expressions for four field string corrections are derived.
Dirac-Kaehler Theory and Massless Fields
Pletyukhov, V. A.; Strazhev, V. I.
2010-03-24
Three massless limits of the Dirac-Kaehler theory are considered. It is shown that the Dirac-Kaehler equation for massive particles can be represented as a result of the gauge-invariant mixture (topological interaction) of the above massless fields.
Magnetic fields in Local Group dwarf irregulars
NASA Astrophysics Data System (ADS)
Chyży, K. T.; Weżgowiec, M.; Beck, R.; Bomans, D. J.
2011-05-01
Aims: We wish to clarify whether strong magnetic fields can be effectively generated in typically low-mass dwarf galaxies and to assess the role of dwarf galaxies in the magnetization of the Universe. Methods: We performed a search for radio emission and magnetic fields in an unbiased sample of 12 Local Group (LG) irregular and dwarf irregular galaxies with the 100-m Effelsberg telescope at 2.64 GHz. Three galaxies were detected. A higher frequency (4.85 GHz) was used to search for polarized emission in five dwarfs that are the most luminous ones in the infrared domain, of which three were detected. Results: Magnetic fields in LG dwarfs are weak, with a mean value of the total field strength of <4.2 ± 1.8 μG, three times lower than in the normal spirals. The strongest field among all LG dwarfs of 10 μG (at 2.64 GHz) is observed in the starburst dwarf IC 10. The production of total magnetic fields in dwarf systems appears to be regulated mainly by the star-formation surface density (with the power-law exponent of 0.30 ± 0.04) or by the gas surface density (with the exponent 0.47 ± 0.09). In addition, we find systematically stronger fields in objects of higher global star-formation rate. The dwarf galaxies follow a similar far-infrared relationship (with a slope of 0.91 ± 0.08) to that determined for high surface brightness spiral galaxies. The magnetic field strength in dwarf galaxies does not correlate with their maximum rotational velocity, indicating that a small-scale rather than a large-scale dynamo process is responsible for producting magnetic fields in dwarfs. If magnetization of the Universe by galactic outflows is coeval with its metal enrichment, we show that more massive objects (such as Lyman break galaxies) can efficiently magnetize the intergalactic medium with a magnetic field strength of about 0.8 nG out to a distance of 160-530 kpc at redshifts 5-3, respectively. Magnetic fields that are several times weaker and shorter magnetization
A periodic table of effective field theories
NASA Astrophysics Data System (ADS)
Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Shen, Chia-Hsien; Trnka, Jaroslav
2017-02-01
We systematically explore the space of scalar effective field theories (EFTs) consistent with a Lorentz invariant and local S-matrix. To do so we define an EFT classification based on four parameters characterizing 1) the number of derivatives per interaction, 2) the soft properties of amplitudes, 3) the leading valency of the interactions, and 4) the spacetime dimension. Carving out the allowed space of EFTs, we prove that exceptional EFTs like the non-linear sigma model, Dirac-Born-Infeld theory, and the special Galileon lie precisely on the boundary of allowed theory space. Using on-shell momentum shifts and recursion relations, we prove that EFTs with arbitrarily soft behavior are forbidden and EFTs with leading valency much greater than the spacetime dimension cannot have enhanced soft behavior. We then enumerate all single scalar EFTs in d < 6 and verify that they correspond to known theories in the literature. Our results suggest that the exceptional theories are the natural EFT analogs of gauge theory and gravity because they are one-parameter theories whose interactions are strictly dictated by properties of the S-matrix.
Group-III Nitride Field Emitters
NASA Technical Reports Server (NTRS)
Bensaoula, Abdelhak; Berishev, Igor
2008-01-01
Field-emission devices (cold cathodes) having low electron affinities can be fabricated through lattice-mismatched epitaxial growth of nitrides of elements from group III of the periodic table. Field emission of electrons from solid surfaces is typically utilized in vacuum microelectronic devices, including some display devices. The present field-emission devices and the method of fabricating them were developed to satisfy needs to reduce the cost of fabricating field emitters, make them compatible with established techniques for deposition of and on silicon, and enable monolithic integration of field emitters with silicon-based driving circuitry. In fabricating a device of this type, one deposits a nitride of one or more group-III elements on a substrate of (111) silicon or other suitable material. One example of a suitable deposition process is chemical vapor deposition in a reactor that contains plasma generated by use of electron cyclotron resonance. Under properly chosen growth conditions, the large mismatch between the crystal lattices of the substrate and the nitride causes strains to accumulate in the growing nitride film, such that the associated stresses cause the film to crack. The cracks lie in planes parallel to the direction of growth, so that the growing nitride film becomes divided into microscopic growing single-crystal columns. The outer ends of the fully-grown columns can serve as field-emission tips. By virtue of their chemical compositions and crystalline structures, the columns have low work functions and high electrical conductivities, both of which are desirable for field emission of electrons. From examination of transmission electron micrographs of a prototype device, the average column width was determined to be about 100 nm and the sharpness of the tips was determined to be characterized by a dimension somewhat less than 100 nm. The areal density of the columns was found to about 5 x 10(exp 9)/sq cm . about 4 to 5 orders of magnitude
A computational theory of visual receptive fields.
Lindeberg, Tony
2013-12-01
A receptive field constitutes a region in the visual field where a visual cell or a visual operator responds to visual stimuli. This paper presents a theory for what types of receptive field profiles can be regarded as natural for an idealized vision system, given a set of structural requirements on the first stages of visual processing that reflect symmetry properties of the surrounding world. These symmetry properties include (i) covariance properties under scale changes, affine image deformations, and Galilean transformations of space-time as occur for real-world image data as well as specific requirements of (ii) temporal causality implying that the future cannot be accessed and (iii) a time-recursive updating mechanism of a limited temporal buffer of the past as is necessary for a genuine real-time system. Fundamental structural requirements are also imposed to ensure (iv) mutual consistency and a proper handling of internal representations at different spatial and temporal scales. It is shown how a set of families of idealized receptive field profiles can be derived by necessity regarding spatial, spatio-chromatic, and spatio-temporal receptive fields in terms of Gaussian kernels, Gaussian derivatives, or closely related operators. Such image filters have been successfully used as a basis for expressing a large number of visual operations in computer vision, regarding feature detection, feature classification, motion estimation, object recognition, spatio-temporal recognition, and shape estimation. Hence, the associated so-called scale-space theory constitutes a both theoretically well-founded and general framework for expressing visual operations. There are very close similarities between receptive field profiles predicted from this scale-space theory and receptive field profiles found by cell recordings in biological vision. Among the family of receptive field profiles derived by necessity from the assumptions, idealized models with very good qualitative
Extending Gurwitsch's field theory of consciousness.
Yoshimi, Jeff; Vinson, David W
2015-07-01
Aron Gurwitsch's theory of the structure and dynamics of consciousness has much to offer contemporary theorizing about consciousness and its basis in the embodied brain. On Gurwitsch's account, as we develop it, the field of consciousness has a variable sized focus or "theme" of attention surrounded by a structured periphery of inattentional contents. As the field evolves, its contents change their status, sometimes smoothly, sometimes abruptly. Inner thoughts, a sense of one's body, and the physical environment are dominant field contents. These ideas can be linked with (and help unify) contemporary theories about the neural correlates of consciousness, inattention, the small world structure of the brain, meta-stable dynamics, embodied cognition, and predictive coding in the brain.
C*-algebraic scattering theory and explicitly solvable quantum field theories
NASA Astrophysics Data System (ADS)
Warchall, Henry A.
1985-06-01
A general theoretical framework is developed for the treatment of a class of quantum field theories that are explicitly exactly solvable, but require the use of C*-algebraic techniques because time-dependent scattering theory cannot be constructed in any one natural representation of the observable algebra. The purpose is to exhibit mechanisms by which inequivalent representations of the observable algebra can arise in quantum field theory, in a setting free of other complications commonly associated with the specification of dynamics. One of two major results is the development of necessary and sufficient conditions for the concurrent unitary implementation of two automorphism groups in a class of quasifree representations of the algebra of the canonical commutation relations (CCR). The automorphism groups considered are induced by one-parameter groups of symplectic transformations on the classical phase space over which the Weyl algebra of the CCR is built; each symplectic group is conjugate by a fixed symplectic transformation to a one-parameter unitary group. The second result, an analog to the Birman-Belopol'skii theorem in two-Hilbert-space scattering theory, gives sufficient conditions for the existence of Mo/ller wave morphisms in theories with time-development automorphism groups of the above type. In a paper which follows, this framework is used to analyze a particular model system for which wave operators fail to exist in any natural representation of the observable algebra, but for which wave morphisms and an associated S matrix are easily constructed.
Inflation and deformation of conformal field theory
Garriga, Jaume; Urakawa, Yuko E-mail: yurakawa@ffn.ub.es
2013-07-01
It has recently been suggested that a strongly coupled phase of inflation may be described holographically in terms of a weakly coupled quantum field theory (QFT). Here, we explore the possibility that the wave function of an inflationary universe may be given by the partition function of a boundary QFT. We consider the case when the field theory is a small deformation of a conformal field theory (CFT), by the addition of a relevant operator O, and calculate the primordial spectrum predicted in the corresponding holographic inflation scenario. Using the Ward-Takahashi identity associated with Weyl rescalings, we derive a simple relation between correlators of the curvature perturbation ζ and correlators of the deformation operator O at the boundary. This is done without specifying the bulk theory of gravitation, so that the result would also apply to cases where the bulk dynamics is strongly coupled. We comment on the validity of the Suyama-Yamaguchi inequality, relating the bi-spectrum and tri-spectrum of the curvature perturbation.
Recursion equations in gauge field theories
NASA Astrophysics Data System (ADS)
Migdal, A. A.
An approximate recursion equation is formulated, describing the scale transformation of the effective action of a gauge field. In two-dimensional space-time the equation becomes exact. In four-dimensional theories it reproduces asymptotic freedom to an accuracy of 30% in the coefficients of the β-function. In the strong-coupling region the β-function remains negative and this results in an asymptotic prison in the infrared region. Possible generalizations and applications to the quark-gluon gauge theory are discussed.
Alpha particles in effective field theory
Caniu, C.
2014-11-11
Using an effective field theory for alpha (α) particles at non-relativistic energies, we calculate the strong scattering amplitude modified by Coulomb corrections for a system of two αs. For the strong interaction, we consider a momentum-dependent interaction which, in contrast to an energy dependent interaction alone [1], could be more useful in extending the theory to systems with more than two α particles. We will present preliminary results of our EFT calculations for systems with two alpha particles.
Group-kinetic theory of turbulence
NASA Technical Reports Server (NTRS)
Tchen, C. M.
1986-01-01
The two phases are governed by two coupled systems of Navier-Stokes equations. The couplings are nonlinear. These equations describe the microdynamical state of turbulence, and are transformed into a master equation. By scaling, a kinetic hierarchy is generated in the form of groups, representing the spectral evolution, the diffusivity and the relaxation. The loss of memory in formulating the relaxation yields the closure. The network of sub-distributions that participates in the relaxation is simulated by a self-consistent porous medium, so that the average effect on the diffusivity is to make it approach equilibrium. The kinetic equation of turbulence is derived. The method of moments reverts it to the continuum. The equation of spectral evolution is obtained and the transport properties are calculated. In inertia turbulence, the Kolmogoroff law for weak coupling and the spectrum for the strong coupling are found. As the fluid analog, the nonlinear Schrodinger equation has a driving force in the form of emission of solitons by velocity fluctuations, and is used to describe the microdynamical state of turbulence. In order for the emission together with the modulation to participate in the transport processes, the non-homogeneous Schrodinger equation is transformed into a homogeneous master equation. By group-scaling, the master equation is decomposed into a system of transport equations, replacing the Bogoliubov system of equations of many-particle distributions. It is in the relaxation that the memory is lost when the ensemble of higher-order distributions is simulated by an effective porous medium. The closure is thus found. The kinetic equation is derived and transformed into the equation of spectral flow.
Free □ k scalar conformal field theory
NASA Astrophysics Data System (ADS)
Brust, Christopher; Hinterbichler, Kurt
2017-02-01
We consider the generalizations of the free U( N ) and O( N ) scalar conformal field theories to actions with higher powers of the Laplacian □ k , in general dimension d. We study the spectra, Verma modules, anomalies and OPE of these theories. We argue that in certain d and k, the spectrum contains zero norm operators which are both primary and descendant, as well as extension operators which are neither primary nor descendant. In addition, we argue that in even dimensions d ≤ 2 k, there are well-defined operator algebras which are related to the □ k theories and are novel in that they have a finite number of single-trace states.
Operator algebra in logarithmic conformal field theory
Nagi, Jasbir
2005-10-15
For some time now, conformal field theories in two dimensions have been studied as integrable systems. Much of the success of these studies is related to the existence of an operator algebra of the theory. In this paper, some of the extensions of this machinery to the logarithmic case are studied and used. More precisely, from Moebius symmetry constraints, the generic three- and four-point functions of logarithmic quasiprimary fields are calculated in closed form for arbitrary Jordan rank. As an example, c=0 disordered systems with nondegenerate vacua are studied. With the aid of two-, three-, and four-point functions, the operator algebra is obtained and associativity of the algebra studied.
Magnetic fields and density functional theory
Salsbury Jr., Freddie
1999-02-01
A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.
Effective Field Theory for Rydberg Polaritons
NASA Astrophysics Data System (ADS)
Gullans, M. J.; Thompson, J. D.; Wang, Y.; Liang, Q.-Y.; Vuletić, V.; Lukin, M. D.; Gorshkov, A. V.
2016-09-01
We develop an effective field theory (EFT) to describe the few- and many-body propagation of one-dimensional Rydberg polaritons. We show that the photonic transmission through the Rydberg medium can be found by mapping the propagation problem to a nonequilibrium quench, where the role of time and space are reversed. We include effective range corrections in the EFT and show that they dominate the dynamics near scattering resonances in the presence of deep bound states. Finally, we show how the long-range nature of the Rydberg-Rydberg interactions induces strong effective N -body interactions between Rydberg polaritons. These results pave the way towards studying nonperturbative effects in quantum field theories using Rydberg polaritons.
Effective Field Theory for Rydberg Polaritons
Gullans, M. J.; Thompson, J. D.; Wang, Y.; Liang, Q.-Y.; Vuletić, V.; Lukin, M. D.; Gorshkov, A. V.
2016-01-01
We develop an effective field theory (EFT) to describe the few- and many-body propagation of one dimensional Rydberg polaritons. We show that the photonic transmission through the Rydberg medium can be found by mapping the propagation problem to a non-equilibrium quench, where the role of time and space are reversed. We include effective range corrections in the EFT and show that they dominate the dynamics near scattering resonances in the presence of deep bound states. Finally, we show how the long-range nature of the Rydberg-Rydberg interactions induces strong effective N-body interactions between Rydberg polaritons. These results pave the way towards studying non-perturbative effects in quantum field theories using Rydberg polaritons. PMID:27661685
Quantitative field theory of the glass transition
Franz, Silvio; Jacquin, Hugo; Parisi, Giorgio; Urbani, Pierfrancesco; Zamponi, Francesco
2012-01-01
We develop a full microscopic replica field theory of the dynamical transition in glasses. By studying the soft modes that appear at the dynamical temperature, we obtain an effective theory for the critical fluctuations. This analysis leads to several results: we give expressions for the mean field critical exponents, and we analytically study the critical behavior of a set of four-points correlation functions, from which we can extract the dynamical correlation length. Finally, we can obtain a Ginzburg criterion that states the range of validity of our analysis. We compute all these quantities within the hypernetted chain approximation for the Gibbs free energy, and we find results that are consistent with numerical simulations. PMID:23112202
Superconformal field theories from M-theory crystal lattices
NASA Astrophysics Data System (ADS)
Lee, Sangmin
2007-05-01
We propose a brane configuration for the (2+1)d, N=2 superconformal theories (CFT3) arising from M2 branes probing toric Calabi-Yau 4-fold cones, using a T-duality transformation of M theory. We obtain intersections of M5-branes on a three-torus which form a 3d bipartite crystal lattice in a way similar to the 2d dimer models for CFT4. The fundamental fields of the CFT3 are M2-brane discs localized around the intersections, and the superpotential terms are identified with the atoms of the crystal. The model correctly reproduces the Bogomol’nyi-Prasad-Sommerfield (BPS) spectrum of mesons.
The impact of renormalization group theory on magnetism
NASA Astrophysics Data System (ADS)
Köbler, U.; Hoser, A.
2007-11-01
The basic issues of renormalization group (RG) theory, i.e. universality, crossover phenomena, relevant interactions etc. are verified experimentally on magnetic materials. Universality is demonstrated on account of the saturation of the magnetic order parameter for T ↦ 0. Universal means that the deviations with respect to saturation at T = 0 can perfectly be described by a power function of absolute temperature with an exponent ɛ that is independent of spin structure and lattice symmetry. Normally the Tɛ function holds up to ~0.85Tc where crossover to the critical power function occurs. Universality for T ↦ 0 cannot be explained on the basis of the material specific magnon dispersions that are due to atomistic symmetry. Instead, continuous dynamic symmetry has to be assumed. The quasi particles of the continuous symmetry can be described by plane waves and have linear dispersion in all solids. This then explains universality. However, those quasi particles cannot be observed using inelastic neutron scattering. The principle of relevance is demonstrated using the competition between crystal field interaction and exchange interaction as an example. If the ratio of crystal field interaction to exchange interaction is below some threshold value the local crystal field is not relevant under the continuous symmetry of the ordered state and the saturation moment of the free ion is observed for T ↦ 0. Crossover phenomena either between different exponents or between discrete changes of the pre-factor of the Tɛ function are demonstrated for the spontaneous magnetization and for the heat capacity.
Higher spin double field theory: a proposal
NASA Astrophysics Data System (ADS)
Bekaert, Xavier; Park, Jeong-Hyuck
2016-07-01
We construct a double field theory coupled to the fields present in Vasiliev's equations. Employing the "semi-covariant" differential geometry, we spell a functional in which each term is completely covariant with respect to O(4, 4) T-duality, doubled diffeomorphisms, Spin(1, 3) local Lorentz symmetry and, separately, HS(4) higher spin gauge symmetry. We identify a minimal set of BPS-like conditions whose solutions automatically satisfy the full Euler-Lagrange equations. As such a solution, we derive a linear dilaton vacuum. With extra algebraic constraints further supplemented, the BPS-like conditions reduce to the bosonic Vasiliev equations.
Generalized IIB supergravity from exceptional field theory
NASA Astrophysics Data System (ADS)
Baguet, Arnaud; Magro, Marc; Samtleben, Henning
2017-03-01
The background underlying the η-deformed AdS 5 × S 5 sigma-model is known to satisfy a generalization of the IIB supergravity equations. Their solutions are related by T-duality to solutions of type IIA supergravity with non-isometric linear dilaton. We show how the generalized IIB supergravity equations can be naturally obtained from exceptional field theory. Within this manifestly duality covariant formulation of maximal supergravity, the generalized IIB supergravity equations emerge upon imposing on the fields a simple Scherk-Schwarz ansatz which respects the section constraint.
The Supersymmetric Effective Field Theory of Inflation
NASA Astrophysics Data System (ADS)
Delacrétaz, Luca V.; Gorbenko, Victor; Senatore, Leonardo
2017-03-01
We construct the Supersymmetric Effective Field Theory of Inflation, that is the most general theory of inflationary fluctuations when time-translations and supersymmetry are spontaneously broken. The non-linear realization of these invariances allows us to define a complete SUGRA multiplet containing the graviton, the gravitino, the Goldstone of time translations and the Goldstino, with no auxiliary fields. Going to a unitary gauge where only the graviton and the gravitino are present, we write the most general Lagrangian built out of the fluctuations of these fields, invariant under time-dependent spatial diffeomorphisms, but softly-breaking time diffeomorphisms and gauged SUSY. With a suitable Stückelberg transformation, we introduce the Goldstone boson of time translation and the Goldstino of SUSY. No additional dynamical light field is needed. In the high energy limit, larger than the inflationary Hubble scale for the Goldstino, these fields decouple from the graviton and the gravitino, greatly simplifying the analysis in this regime. We study the phenomenology of this Lagrangian. The Goldstino can have a non-relativistic dispersion relation. Gravitino and Goldstino affect the primordial curvature perturbations at loop level. The UV modes running in the loops generate three-point functions which are degenerate with the ones coming from operators already present in the absence of supersymmetry. Their size is potentially as large as corresponding to f NL equil., orthog. ˜ 1 or, for particular operators, even ≫ 1. The non-degenerate contribution from modes of order H is estimated to be very small.
Backreacted axion field ranges in string theory
NASA Astrophysics Data System (ADS)
Baume, Florent; Palti, Eran
2016-08-01
String theory axions are interesting candidates for fields whose potential might be controllable over super-Planckian field ranges and therefore as possible candidates for inflatons in large field inflation. Axion monodromy scenarios are setups where the axion shift symmetry is broken by some effect such that the axion can traverse a large number of periods potentially leading to super-Planckian excursions. We study such scenarios in type IIA string theory where the axion shift symmetry is broken by background fluxes. In particular we calculate the backreaction of the energy density induced by the axion vacuum expectation value on its own field space metric. We find universal behaviour for all the compactifications studied where up to a certain critical axion value there is only a small backreaction effect. Beyond the critical value the backreaction is strong and implies that the proper field distance as measured by the backreacted metric increases at best logarithmically with the axion vev, thereby placing strong limitations on extending the field distance any further. The critical axion value can be made arbitrarily large by the choice of fluxes. However the backreaction of these fluxes on the axion field space metric ensures a precise cancellation such that the proper field distance up to the critical axion value is flux independent and remains sub-Planckian. We also study an axion alignment scenario for type IIA compactifications on a twisted torus with four fundamental axions mixing to leave an axion with an effective decay constant which is flux dependent. There is a choice of fluxes for which the alignment parameter controlling the effective decay constant is unconstrained by tadpoles and can in principle lead to an arbitrarily large effective decay constant. However we show that these fluxes backreact on the fundamental decay constants so as to precisely cancel any enhancement leaving a sub-Planckian effective decay constant.
Hamiltonian formulation of string field theory
NASA Astrophysics Data System (ADS)
Siopsis, George
1987-09-01
Witten's string field theory is quantized in the hamiltonian formalism. The constraints are solved and the hamiltonian is expressed in terms of only physical degrees of freedom. Thus, no Faddeev-Popov ghosts are introduced. Instead, the action contains terms of arbitrarily high order in the string functionals. Agreement with the standard results is demonstrated by an explicit calculation of the residues of the first few poles of the four-tachyon tree amplitude.
Superconformal partial waves in Grassmannian field theories
NASA Astrophysics Data System (ADS)
Doobary, Reza; Heslop, Paul
2015-12-01
We derive superconformal partial waves for all scalar four-point functions on a super Grassmannian space Gr( m| n, 2 m|2 n) for all m, n. This family of four-point functions includes those of all (arbitrary weight) half BPS operators in both N=4 SYM ( m = n = 2) and in N = 2 superconformal field theories in four dimensions ( m = 2 , n = 1) on analytic superspace. It also includes four-point functions of all (arbitrary dimension) scalar fields in non-supersymmetric conformal field theories ( m = 2 , n = 0) on Minkowski space, as well as those of a certain class of representations of the compact SU(2 n) coset spaces. As an application we then specialise to N=4 SYM and use these results to perform a detailed superconformal partial wave analysis of the four-point functions of arbitrary weight half BPS operators. We discuss the non-trivial separation of protected and unprotected sectors for the <2222>, <2233> and <3333> cases in an SU( N) gauge theory at finite N. The <2233> correlator predicts a non-trivial protected twist four sector for <3333> which we can completely determine using the knowledge that there is precisely one such protected twist four operator for each spin.
Fermionic ghosts in Moyal string field theory
NASA Astrophysics Data System (ADS)
Bars, Itzhak; Kishimoto, Isao; Matsuo, Yutaka
2003-07-01
We complete the construction of the Moyal star formulation of bosonic open string field theory (MSFT) by providing a detailed study of the fermionic ghost sector. In particular, as in the case of the matter sector, (1) we construct a map from Witten's star product to the Moyal product, (2) we propose a regularization scheme which is consistent with the matter sector and (3) as a check of the formalism, we derive the ghost Neumann coefficients algebraically directly from the Moyal product. The latter satisfy the Gross-Jevicki nonlinear relations even in the presence of the regulator, and when the regulator is removed they coincide numerically with the expression derived from conformal field theory. After this basic construction, we derive a regularized action of string field theory in the Siegel gauge and define the Feynman rules. We give explicitly the analytic expression of the off-shell four point function for tachyons, including the ghost contribution. Some of the results in this paper have already been used in our previous publications. This paper provides the technical details of the computations which were omitted there.
Heavy Quarks, QCD, and Effective Field Theory
Thomas Mehen
2012-10-09
The research supported by this OJI award is in the area of heavy quark and quarkonium production, especially the application Soft-Collinear E ective Theory (SCET) to the hadronic production of quarkonia. SCET is an e ffective theory which allows one to derive factorization theorems and perform all order resummations for QCD processes. Factorization theorems allow one to separate the various scales entering a QCD process, and in particular, separate perturbative scales from nonperturbative scales. The perturbative physics can then be calculated using QCD perturbation theory. Universal functions with precise fi eld theoretic de nitions describe the nonperturbative physics. In addition, higher order perturbative QCD corrections that are enhanced by large logarithms can be resummed using the renormalization group equations of SCET. The applies SCET to the physics of heavy quarks, heavy quarkonium, and similar particles.
Nonperturbative studies in quantum field theory
Abada, A.
1992-01-01
This dissertation is composed of three different research topics. The first part deals with the Study of the so-called local lattice Yukawa theory. The motivation for this study is to investigate the interior of the phase diagram of this theory. A strong y expansion (y being the bare Yukawa coupling) is performed of the partition function and show that within the (finite) range of convergence of the series expansion, the lattice Yukawa theory is equivalent to a purely bosonic theory, with a shifted action. The author explicitly calculated the shifted action to the fourth order in 1/y and find that it is composed of competing interactions. This suggests that away from y = [infinity] towards the interior of the phase diagram, there is a more complicated ordering than simple ferromagnetic or antiferromagnetic. In the second part, the question is addressed of formation of bound states out of constituent fields in an exactly soluble theory, i.e. multifermion electro-dynamics in two space-time dimensions. The author exactly calculates the correlation function corresponding to a neutral composite fermion operator and discuss the pole structure of its Fourier transform. It does not exhibit a simple pole in p[sup 2], hence the corresponding neutral composite operator does not create an asymptotic state in the spectrum of the theory. In part three, the author puts multifermion QED[sub 2] in a heat bath and address the same question as in part two. The author first exactly calculates a bosonic correlation function at finite temperature and density, and discuss its behavior. The author then exactly calculates the correlation function corresponding to the neutral composite fermion operator at finite temperature and density and discusses its behavior. It is concluded that the temperature does not help the composite fermion operator create a particle in the spectrum of the theory.
Reading Discussion Groups for Teachers: Connecting Theory to Practice
ERIC Educational Resources Information Center
Fenton-Smith, Ben; Stillwell, Christopher
2011-01-01
This article explores how teachers can engage with ideas (research findings, theory, and professional knowledge) through participation in a reading discussion group. Focusing on one group formed by English language teachers at a Japanese university, the study employs survey data, attendance statistics, and observational notes regarding the group's…
A Grounded Theory of Western-Trained Asian Group Leaders Leading Groups in Asia
ERIC Educational Resources Information Center
Taephant, Nattasuda; Rubel, Deborah; Champe, Julia
2015-01-01
This grounded theory research explored the experiences of Western-trained Asian group leaders leading groups in Asia. A total of 6 participants from Japan, Taiwan, and Thailand were interviewed 3 times over 9 months. The recursive process of data collection and analysis yielded substantive theory describing the participants' process of reconciling…
Emergent coherent structures in nonequilibrium field theory
NASA Astrophysics Data System (ADS)
Thorarinson, Joel Larus Marvin
2008-10-01
In this thesis we study the properties of time-dependent, nontopological configurations and their effect on the macroscopic properties of a system described by a nonlinear field theory. These structures seem to be ubiquitous in relativistic field theories with symmetry breaking scenarios and since they drastically change the power spectrum, understanding their properties and lifetimes is essential for characterization of the equilibration time scales of a given system. To understand the mechanisms of their creation we rely on large scale computations to solve the fully nonlinear equations of motion. By using both Langevin thermalization techniques and various ansatz we find information about both the individual formation and stability properties of these structures and their effect on global observables such as the decay rate of a metastable vacuum. Each of these aspects contains surprises and radical departures from the linearized theories. We also show examples of how these structures can be examined in momentum space from computing several correlation functions. We extend 2d results on the effect of these emergent structures to the decay rate of a false vacuum to 3d and confirm that these time-dependent structures modify the decay, after a quench, to a power law in pure scalar theories. Adding gauge fields, we present new time dependent nontopological solutions in the 2d Abelian Higgs model which show the creation of oscillons from vortex antivortex annihilations. A phase transition in configuration space is then constructed from the stability properties of these oscillons in parameter space. Similarly, in 3 d we show that oscillons may be formed through toroidal ux-tube annihilations. Finally, these properties are shown to also apply to more complex situations, such as the condensed proton-neutron system, which exhibits all the previous oscillon results as well as a new nontrivial vortex-vortex bound state.
Theory of gain in group-III nitride lasers
Chow, W.W.; Wright, A.F.; Girndt, A.
1997-06-01
A microscopic theory of gain in a group-III nitride quantum well laser is presented. The approach, which treats carrier correlations at the level of quantum kinetic theory, gives a consistent account of plasma and excitonic effects in an inhomogeneously broadened system.
Practicing Social Movement Theory in Case Study Groups
ERIC Educational Resources Information Center
Ormrod, James S.
2011-01-01
This article evaluates the use of a "case study group" method for teaching social movement theory. The aim was to give students the opportunity to practice theorizing actively rather than simply learning theory passively. The method provides this by requiring students to undertake case studies on social movements of their choice for the…
An Intuitive Approach to Group Representation Theory, II.
ERIC Educational Resources Information Center
Wolbarst, A. B.
1979-01-01
This is the second of several papers which attempts to introduce group representation theory to students of molecular or solid-state physics in as intuitive and simple a fashion as possible. (Author/BB)
Haag's Theorem and Parameterized Quantum Field Theory
NASA Astrophysics Data System (ADS)
Seidewitz, Edwin
2017-01-01
``Haag's theorem is very inconvenient; it means that the interaction picture exists only if there is no interaction''. In traditional quantum field theory (QFT), Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. But the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field, but which must still account for interactions. So, the usual derivation of the scattering matrix in QFT is mathematically ill defined. Nevertheless, perturbative QFT is currently the only practical approach for addressing realistic scattering, and it has been very successful in making empirical predictions. This success can be understood through an alternative derivation of the Dyson series in a covariant formulation of QFT using an invariant, fifth path parameter in addition to the usual four position parameters. The parameterization provides an additional degree of freedom that allows Haag's Theorem to be avoided, permitting the consistent use of a form of interaction picture in deriving the Dyson expansion. The extra symmetry so introduced is then broken by the choice of an interacting vacuum.
Causality constraints in conformal field theory
Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
2016-05-17
Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms in the low energy Lagrangian. In d dimensional conformal field theory, we show how such constraints are encoded in crossing symmetry of Euclidean correlators, and derive analogous constraints directly from the conformal bootstrap (analytically). The bootstrap setup is a Lorentzian four-point function corresponding to propagation through a shockwave. Crossing symmetry fixes the signs of certain log terms that appear in the conformal block expansion, which constrains the interactions of low-lying operators. As an application, we use the bootstrap to rederive the well knownmore » sign constraint on the (Φ)4 coupling in effective field theory, from a dual CFT. We also find constraints on theories with higher spin conserved currents. As a result, our analysis is restricted to scalar correlators, but we argue that similar methods should also impose nontrivial constraints on the interactions of spinning operators« less
Bayesian parameter estimation for effective field theories
NASA Astrophysics Data System (ADS)
Wesolowski, S.; Klco, N.; Furnstahl, R. J.; Phillips, D. R.; Thapaliya, A.
2016-07-01
We present procedures based on Bayesian statistics for estimating, from data, the parameters of effective field theories (EFTs). The extraction of low-energy constants (LECs) is guided by theoretical expectations in a quantifiable way through the specification of Bayesian priors. A prior for natural-sized LECs reduces the possibility of overfitting, and leads to a consistent accounting of different sources of uncertainty. A set of diagnostic tools is developed that analyzes the fit and ensures that the priors do not bias the EFT parameter estimation. The procedures are illustrated using representative model problems, including the extraction of LECs for the nucleon-mass expansion in SU(2) chiral perturbation theory from synthetic lattice data.
The effective field theory of dark energy
Gubitosi, Giulia; Vernizzi, Filippo; Piazza, Federico E-mail: fpiazza@apc.univ-paris7.fr
2013-02-01
We propose a universal description of dark energy and modified gravity that includes all single-field models. By extending a formalism previously applied to inflation, we consider the metric universally coupled to matter fields and we write in terms of it the most general unitary gauge action consistent with the residual unbroken symmetries of spatial diffeomorphisms. Our action is particularly suited for cosmological perturbation theory: the background evolution depends on only three operators. All other operators start at least at quadratic order in the perturbations and their effects can be studied independently and systematically. In particular, we focus on the properties of a few operators which appear in non-minimally coupled scalar-tensor gravity and galileon theories. In this context, we study the mixing between gravity and the scalar degree of freedom. We assess the quantum and classical stability, derive the speed of sound of fluctuations and the renormalization of the Newton constant. The scalar can always be de-mixed from gravity at quadratic order in the perturbations, but not necessarily through a conformal rescaling of the metric. We show how to express covariant field-operators in our formalism and give several explicit examples of dark energy and modified gravity models in our language. Finally, we discuss the relation with the covariant EFT methods recently appeared in the literature.
Unexpected connections between Burnside groups and knot theory
Dabkowski, Mieczyslaw K.; Przytycki, Józef H.
2004-01-01
In classical knot theory and the theory of quantum invariants substantial effort was directed toward the search for unknotting moves on links. We solve, in this article, several classical problems concerning unknotting moves. Our approach uses a concept, Burnside groups of links, that establishes an unexpected relationship between knot theory and group theory. Our method has the potential to be used in computational biology in the analysis of DNA via tangle embedding theory, as developed by D. W. Sumners [Sumners, D. W., ed. (1992) New Scientific Applications of Geometry and Topology (Am Math. Soc., Washington, DC) and Ernst, C. & Sumners, D. W. (1999) Math. Proc. Cambridge Philos. Soc. 126, 23–36]. PMID:15576510
Pomeron-Odderon interactions in a Reggeon field theory
NASA Astrophysics Data System (ADS)
Bartels, Jochen; Contreras, Carlos; Vacca, Gian Paolo
2017-01-01
In this paper we extend our recent nonperturbative functional renormalization group analysis of Reggeon field theory to the interactions of Pomeron and Odderon fields. We establish the existence of a fixed point and its universal properties, which exhibits a novel symmetry structure in the space of Odderon-Pomeron interactions. As in our previous analysis, this part of our program aims at the investigation of the IR limit of Reggeon field theory (the limit of high energies and large transverse distances). It should be seen in the broader context of trying to connect the nonperturbative infrared region (large transverse distances) with the UV region of small transverse distances where the high energy limit of perturbative QCD applies. We briefly discuss the implications of our findings for the existence of an Odderon in high energy scattering.
Consistent Kaluza-Klein truncations via exceptional field theory
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Samtleben, Henning
2015-01-01
We present the generalized Scherk-Schwarz reduction ansatz for the full supersymmetric exceptional field theory in terms of group valued twist matrices subject to consistency equations. With this ansatz the field equations precisely reduce to those of lower-dimensional gauged supergravity parametrized by an embedding tensor. We explicitly construct a family of twist matrices as solutions of the consistency equations. They induce gauged supergravities with gauge groups SO( p, q) and CSO( p, q, r). Geometrically, they describe compactifications on internal spaces given by spheres and (warped) hyperboloides H p,q , thus extending the applicability of generalized Scherk-Schwarz reductions beyond homogeneous spaces. Together with the dictionary that relates exceptional field theory to D = 11 and IIB supergravity, respectively, the construction defines an entire new family of consistent truncations of the original theories. These include not only compactifications on spheres of different dimensions (such as AdS5 × S 5), but also various hyperboloid compactifications giving rise to a higher-dimensional embedding of supergravities with non-compact and non-semisimple gauge groups.
Toward a quantum theory of tachyon fields
NASA Astrophysics Data System (ADS)
Schwartz, Charles
2016-03-01
We construct momentum space expansions for the wave functions that solve the Klein-Gordon and Dirac equations for tachyons, recognizing that the mass shell for such fields is very different from what we are used to for ordinary (slower than light) particles. We find that we can postulate commutation or anticommutation rules for the operators that lead to physically sensible results: causality, for tachyon fields, means that there is no connection between space-time points separated by a timelike interval. Calculating the conserved charge and four-momentum for these fields allows us to interpret the number operators for particles and antiparticles in a consistent manner; and we see that helicity plays a critical role for the spinor field. Some questions about Lorentz invariance are addressed and some remain unresolved; and we show how to handle the group representation for tachyon spinors.
Temperature Gradient Field Theory of Nucleation
NASA Astrophysics Data System (ADS)
Das, S.; Ain, W. Q.; Azhari, A.; Prasada Rao, A. K.
2016-02-01
According to the proposed theory, ceramic particles present in molten metal, lose heat at a slower rate than the metallic liquid during cooling. Such condition results in the formation of a spherical thermal gradient field (TGF) around each particle. Hence, the interstitials (low temperature) of such TGFs are the regions to reach the nucleation temperature first, owing to low energy barrier than the liquid-particle interface (higher temperature). Analytics also indicate that the nucleation rate is higher at the TGF interstitials, than at the liquid-particle interface. Such TGF network results in simultaneous nucleation throughout the system, resulting in grain refinement.
Feynman-Schwinger technique in field theories
NASA Astrophysics Data System (ADS)
Şavkli, Çetin
2001-02-01
In these lectures we introduce the Feynman-Schwinger representation method for solying nonperturbative problems in field theory. As an introduction we first give a brief overview of integral equations and path integral methods for solving nonperturbative problems. Then we discuss the Feynman-Schwinger (FSR) representation method with applications to scalar interactions. The FSR approach is a continuum path integral integral approach in terms of covariant trajectories of particles. Using the exact results provided by the FSR approach we test the reliability of commonly used approximations for nonperturbative summation of interactions for few body systems.
A matrix model from string field theory
NASA Astrophysics Data System (ADS)
Zeze, Syoji
2016-09-01
We demonstrate that a Hermitian matrix model can be derived from level truncated open string field theory with Chan-Paton factors. The Hermitian matrix is coupled with a scalar and U(N) vectors which are responsible for the D-brane at the tachyon vacuum. Effective potential for the scalar is evaluated both for finite and large N. Increase of potential height is observed in both cases. The large N matrix integral is identified with a system of N ZZ branes and a ghost FZZT brane.
Exact integrability in quantum field theory
Thacker, H.B.
1980-08-01
The treatment of exactly integrable systems in various branches of two-dimensional classical and quantum physics has recently been placed in a unified framework by the development of the quantum inverse method. This method consolidates a broad range of developments in classical nonlinear wave (soliton) physics, statistical mechanics, and quantum field theory. The essential technique for analyzing exactly integrable quantum systems was invested by Bethe in 1931. The quantum-mechanical extension of the inverse scattering method and its relationship to the methods associated with Bethe's ansatz are examined here. (RWR)
The Effective Field Theory of nonsingular cosmology
NASA Astrophysics Data System (ADS)
Cai, Yong; Wan, Youping; Li, Hai-Guang; Qiu, Taotao; Piao, Yun-Song
2017-01-01
In this paper, we explore the nonsingular cosmology within the framework of the Effective Field Theory (EFT) of cosmological perturbations. Due to the recently proved no-go theorem, any nonsingular cosmological models based on the cubic Galileon suffer from pathologies. We show how the EFT could help us clarify the origin of the no-go theorem, and offer us solutions to break the no-go. Particularly, we point out that the gradient instability can be removed by using some spatial derivative operators in EFT. Based on the EFT description, we obtain a realistic healthy nonsingular cosmological model, and show the perturbation spectrum can be consistent with the observations.
Purely cubic action for string field theory
NASA Technical Reports Server (NTRS)
Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.
1986-01-01
It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.
Theory of microemulsions in a gravitational field
NASA Technical Reports Server (NTRS)
Jeng, J. F.; Miller, Clarence A.
1989-01-01
A theory of microemulsions developed previously is extended to include the effect of a gravitational field. It predicts variation with position of drop size, drop volume fraction, and area per molecule in the surfactant films within a microemulsion phase. Variation in volume fraction is greatest and occurs in such a way that oil content increases with increasing elevation, as has been found experimentally. Large composition variations are predicted within a middle phase microemulsion near optimal conditions because inversion from the water-continuous to the oil-continuous arrangement occurs with increasing elevation. Generally speaking, gravity reduces solubilization within microemulsions and promotes separation of excess phases.
Quantum Corrections and Effective Action in Field Theory
NASA Astrophysics Data System (ADS)
Dalvit, Diego A. R.
1998-07-01
In this Thesis we study quantum corrections to the classical dynamics for mean values in field theory. To that end we make use of the formalism of the closed time path effective action to get real and causal equations of motion. We introduce a coarse grained effective action, which is useful in the study of phase transitions in field theory. We derive an exact renormalization group equation that describes how this action varies with the coarse graining scale. We develop different approximation methods to solve that equation, and we obtain non perturbative improvements to the effective potential for a self interacting scalar field theory. We also discuss the stochastic aspects contained in this action. On the other hand, using the effective action, we find low energy and large distance quantum corrections for the gravitational potential, treating relativity as an effective low energy theory. We include the effect of scalar fields, fermions and gravitons. The inclusion of metric fluctuations causes Einstein semiclassical equations to depend on the gauge fixing parameters, and they are therefore non physical. We solve this problem identifying as a physical observable the trayectory of a test particle. We explicitly show that the geodesic equation for such particle is independent of the arbitrary parameters of the gauge fixing.
Supporting Alternative Strategies for Learning Chemical Applications of Group Theory
ERIC Educational Resources Information Center
Southam, Daniel C.; Lewis, Jennifer E.
2013-01-01
A group theory course for chemists was taught entirely with process oriented guided inquiry learning (POGIL) to facilitate alternative strategies for learning. Students completed a test of one aspect of visuospatial aptitude to determine their individual approaches to solving spatial tasks, and were sorted into groups for analysis on the basis of…
An Application of General System Theory (GST) to Group Therapy.
ERIC Educational Resources Information Center
Matthews, Charles O.
1992-01-01
Demonstrates the compatibility of General System Theory (GST) with the traditional counseling literature in explicating a therapy group's progression through Tuckman's (1965, 1977) developmental stages (forming, storming, norming, performing, and adjourning). Description uses both traditional group literature and GST concepts. (Author/NB)
Causality Is Inconsistent With Quantum Field Theory
Wolf, Fred Alan
2011-11-29
Causality in quantum field theory means the vanishing of commutators for spacelike separated fields (VCSSF). I will show that VCSSF is not tenable. For VCSSF to be tenable, and therefore, to have both retarded and advanced propagators vanish in the elsewhere, a superposition of negative energy antiparticle and positive energy particle propagators, traveling forward in time, and a superposition of negative energy particle and positive energy antiparticle propagators, traveling backward in time, are required. Hence VCSSF predicts non-vanishing probabilities for both negative energy particles in the forward-through-time direction and positive energy antiparticles in the backwards-through-time direction. Therefore, since VCSSF is unrealizable in a stable universe, tachyonic propagation must occur in denial of causality.
The effective field theory treatment of quantum gravity
Donoghue, John F.
2012-09-24
This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity matches this framework and I discuss gravitational examples as well as the limits of the effective field theory. I also discuss the insights from effective field theory on the gravitational effects on running couplings in the perturbative regime.
Continuum regularization of quantum field theory
Bern, Z.
1986-04-01
Possible nonperturbative continuum regularization schemes for quantum field theory are discussed which are based upon the Langevin equation of Parisi and Wu. Breit, Gupta and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the ''fifth-time'' of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, two difficulties arise which, in general, ruins the scheme. One problem is that the superficial quadratic divergences force a bottomless action for the noise. Another difficulty is that stochastic regularization by fifth-time smearing is incompatible with Zwanziger's gauge fixing, which is the only known nonperturbaive covariant gauge fixing for nonabelian gauge theories. Finally, a successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. Hopefully, the scheme will lend itself to nonperturbative analysis. 44 refs., 16 figs.
Thermal field theories and shifted boundary conditions
NASA Astrophysics Data System (ADS)
Giusti, L.; Meyer, H.
The analytic continuation to an imaginary velocity of the canonical partition function of a thermal system expressed in a moving frame has a natural implementation in the Euclidean path-integral formulation in terms of shifted boundary conditions. The Poincare' invariance underlying a relativistic theory implies a dependence of the free-energy on the compact length L_0 and the shift xi only through the combination beta=L_0(1+xi^2)^(1/2). This in turn implies that the energy and the momentum distributions of the thermal theory are related, a fact which is encoded in a set of Ward identities among the correlators of the energy-momentum tensor. The latter have interesting applications in lattice field theory: they offer novel ways to compute thermodynamic potentials, and a set of identities to renormalize non-perturbatively the energy-momentum tensor. At fixed bare parameters the shifted boundary conditions also provide a simple method to vary the temperature in much smaller steps than with the standard procedure.
On Finite Groups and Finite Fields.
ERIC Educational Resources Information Center
Reid, J. D.
1991-01-01
Given a multiplicative group of nonzero elements with order n, the explicit relationship between the number of cyclic subgroups of order d, which divides n, is used in the proof concerning the cyclic nature of that given multiplicative group. (JJK)
Entanglement negativity in quantum field theory.
Calabrese, Pasquale; Cardy, John; Tonni, Erik
2012-09-28
We develop a systematic method to extract the negativity in the ground state of a 1+1 dimensional relativistic quantum field theory, using a path integral formalism to construct the partial transpose ρ(A)(T(2) of the reduced density matrix of a subsystem [formula: see text], and introducing a replica approach to obtain its trace norm which gives the logarithmic negativity E=ln//ρ(A)(T(2))//. This is shown to reproduce standard results for a pure state. We then apply this method to conformal field theories, deriving the result E~(c/4)ln[ℓ(1)ℓ(2)/(ℓ(1)+ℓ(2))] for the case of two adjacent intervals of lengths ℓ(1), ℓ(2) in an infinite system, where c is the central charge. For two disjoint intervals it depends only on the harmonic ratio of the four end points and so is manifestly scale invariant. We check our findings against exact numerical results in the harmonic chain.
Refringence, field theory and normal modes
NASA Astrophysics Data System (ADS)
Barceló, Carlos; Liberati, Stefano; Visser, Matt
2002-06-01
In a previous paper [Barceló C et al 2001 Class. Quantum Grav. 18 3595-610 (Preprint gr-qc/0104001)] we have shown that the occurrence of curved spacetime 'effective Lorentzian geometries' is a generic result of linearizing an arbitrary classical field theory around some nontrivial background configuration. This observation explains the ubiquitous nature of the 'analogue models' for general relativity that have recently been developed based on condensed matter physics. In the simple (single scalar field) situation analysed in our previous paper, there is a single unique effective metric; more complicated situations can lead to bi-metric and multi-metric theories. In the present paper we will investigate the conditions required to keep the situation under control and compatible with experiment - either by enforcing a unique effective metric (as would be required to be strictly compatible with the Einstein equivalence principle), or at the worst by arranging things so that there are multiple metrics that are all 'close' to each other (in order to be compatible with the Eötvös experiment). The algebraically most general situation leads to a physical model whose mathematical description requires an extension of the usual notion of Finsler geometry to a Lorentzian-signature pseudo-Finsler geometry; while this is possibly of some interest in its own right, this particular case does not seem to be immediately relevant for either particle physics or gravitation. The key result is that wide classes of theories lend themselves to an effective metric description. This observation provides further evidence that the notion of 'analogue gravity' is rather generic.
Challenging gender stereotypes: Theory of mind and peer group dynamics.
Mulvey, Kelly Lynn; Rizzo, Michael T; Killen, Melanie
2016-11-01
To investigate the social cognitive skills related to challenging gender stereotypes, children (N = 61, 3-6 years) evaluated a peer who challenged gender stereotypic norms held by the peer's group. Participants with false belief theory of mind (FB ToM) competence were more likely than participants who did not have FB ToM to expect a peer to challenge the group's stereotypes and propose that the group engage in a non-stereotypic activity. Further, participants with FB ToM rated challenging the peer group more positively. Participants without FB ToM did not differentiate between their own and the group's evaluation of challenges to the group's stereotypic norms, but those with ToM competence asserted that they would be more supportive of challenging the group norm than would the peer group. Results reveal the importance of social-cognitive competencies for recognizing the legitimacy of challenging stereotypes, and for understanding one's own and other group perspectives.
Group Dynamics in Janis's Theory of Groupthink: Backward and Forward.
McCauley
1998-02-01
Janis's groupthink theory is an appealing explanation of how group process can get in the way of optimal decision making. Unfortunately, Janis was selective and not always consistent in his application of research in group dynamics. This paper traces groupthink to its theoretical roots in order to suggest how a broader and more consistent use of research in group dynamics can advance understanding of decision-making problems. In particular, the paper explores and reinterprets the groupthink prediction that poor decision making is most likely when group cohesion is based on the personal attractiveness of group members. Copyright 1998 Academic Press.
BOOK REVIEW: Classical Solutions in Quantum Field Theory Classical Solutions in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Mann, Robert
2013-02-01
Quantum field theory has evolved from its early beginnings as a tool for understanding the interaction of light with matter into a rather formidable technical paradigm, one that has successfully provided the mathematical underpinnings of all non-gravitational interactions. Over the eight decades since it was first contemplated the methods have become increasingly more streamlined and sophisticated, yielding new insights into our understanding of the subatomic world and our abilities to make clear and precise predictions. Some of the more elegant methods have to do with non-perturbative and semiclassical approaches to the subject. The chief players here are solitons, instantons, and anomalies. Over the past three decades there has been a steady rise in our understanding of these objects and of our ability to calculate their effects and implications for the rest of quantum field theory. This book is a welcome contribution to this subject. In 12 chapters it provides a clear synthesis of the key developments in these subjects at a level accessible to graduate students that have had an introductory course to quantum field theory. In the author's own words it provides both 'a survey and an overview of this field'. The first half of the book concentrates on solitons--kinks, vortices, and magnetic monopoles--and their implications for the subject. The reader is led first through the simplest models in one spatial dimension, into more sophisticated cases that required more advanced topological methods. The author does quite a nice job of introducing the various concepts as required, and beginning students should be able to get a good grasp of the subject directly from the text without having to first go through the primary literature. The middle part of the book deals with the implications of these solitons for both cosmology and for duality. While the cosmological discussion is quite nice, the discussion on BPS solitons, supersymmetry and duality is rather condensed. It is
Efficient perturbation theory to improve the density matrix renormalization group
NASA Astrophysics Data System (ADS)
Tirrito, Emanuele; Ran, Shi-Ju; Ferris, Andrew J.; McCulloch, Ian P.; Lewenstein, Maciej
2017-02-01
The density matrix renormalization group (DMRG) is one of the most powerful numerical methods available for many-body systems. It has been applied to solve many physical problems, including the calculation of ground states and dynamical properties. In this work, we develop a perturbation theory of the DMRG (PT-DMRG) to greatly increase its accuracy in an extremely simple and efficient way. Using the canonical matrix product state (MPS) representation for the ground state of the considered system, a set of orthogonal basis functions {| ψi> } is introduced to describe the perturbations to the ground state obtained by the conventional DMRG. The Schmidt numbers of the MPS that are beyond the bond dimension cutoff are used to define these perturbation terms. The perturbed Hamiltonian is then defined as H˜i j=< ψi| H ̂|ψj> ; its ground state permits us to calculate physical observables with a considerably improved accuracy compared to the original DMRG results. We benchmark the second-order perturbation theory with the help of a one-dimensional Ising chain in a transverse field and the Heisenberg chain, where the precision of the DMRG is shown to be improved O (10 ) times. Furthermore, for moderate L the errors of the DMRG and PT-DMRG both scale linearly with L-1 (with L being the length of the chain). The linear relation between the dimension cutoff of the DMRG and that of the PT-DMRG at the same precision shows a considerable improvement in efficiency, especially for large dimension cutoffs. In the thermodynamic limit we show that the errors of the PT-DMRG scale with √{L-1}. Our work suggests an effective way to define the tangent space of the ground-state MPS, which may shed light on the properties beyond the ground state. This second-order PT-DMRG can be readily generalized to higher orders, as well as applied to models in higher dimensions.
An integral equation arising in two group neutron transport theory
NASA Astrophysics Data System (ADS)
Cassell, J. S.; Williams, M. M. R.
2003-07-01
An integral equation describing the fuel distribution necessary to maintain a flat flux in a nuclear reactor in two group transport theory is reduced to the solution of a singular integral equation. The formalism developed enables the physical aspects of the problem to be better understood and its relationship with the corresponding diffusion theory model is highlighted. The integral equation is solved by reducing it to a non-singular Fredholm equation which is then evaluated numerically.
Power counting and Wilsonian renormalization in nuclear effective field theory
NASA Astrophysics Data System (ADS)
Valderrama, Manuel Pavón
2016-05-01
Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental — perhaps unknown or unsolvable — high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding of how to apply these ideas to non-perturbative phenomena and in particular to nuclear physics. Here we review a few of these ideas, explain power counting in two-nucleon scattering and reactions with external probes and hint at how to extend the present analysis beyond the two-body problem.
The monster sporadic group and a theory underlying superstring models
Chapline, G.
1996-09-01
The pattern of duality symmetries acting on the states of compactified superstring models reinforces an earlier suggestion that the Monster sporadic group is a hidden symmetry for superstring models. This in turn points to a supersymmetric theory of self-dual and anti-self-dual K3 manifolds joined by Dirac strings and evolving in a 13 dimensional spacetime as the fundamental theory. In addition to the usual graviton and dilaton this theory contains matter-like degrees of freedom resembling the massless states of the heterotic string, thus providing a completely geometric interpretation for ordinary matter. 25 refs.
New Advocacy Groups Shaking up Education Field
ERIC Educational Resources Information Center
Sawchuk, Stephen
2012-01-01
A new generation of education advocacy groups has emerged to play a formidable political role in states and communities across the country. Those groups are shaping policy through aggressive lobbying and campaign activity--an evolution in advocacy that is primed to continue in the 2012 elections and beyond. Though the record of their electoral…
Group theory and biomolecular conformation: I. Mathematical and computational models
Chirikjian, Gregory S
2010-01-01
Biological macromolecules, and the complexes that they form, can be described in a variety of ways ranging from quantum mechanical and atomic chemical models, to coarser grained models of secondary structure and domains, to continuum models. At each of these levels, group theory can be used to describe both geometric symmetries and conformational motion. In this survey, a detailed account is provided of how group theory has been applied across computational structural biology to analyze the conformational shape and motion of macromolecules and complexes. PMID:20827378
ERIC Educational Resources Information Center
Riva, Maria T.; Korinek, Lauri
2004-01-01
Training in group counseling typically includes an academic component, although little has been written about how to teach a group course except for what specific content should be included. This article suggests that while teaching group counseling courses, instructors can intentionally model effective group leader behaviors and use these…
Non-Abelian gauge field theory in scale relativity
Nottale, Laurent; Celerier, Marie-Noeelle; Lehner, Thierry
2006-03-15
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a coupling is expected between displacements in the fractal space-time and the transformations of these scale variables. In previous works, an Abelian gauge theory (electromagnetism) has been derived as a consequence of this coupling for global dilations and/or contractions. We consider here more general transformations of the scale variables by taking into account separate dilations for each of them, which yield non-Abelian gauge theories. We identify these transformations with the usual gauge transformations. The gauge fields naturally appear as a new geometric contribution to the total variation of the action involving these scale variables, while the gauge charges emerge as the generators of the scale transformation group. A generalized action is identified with the scale-relativistic invariant. The gauge charges are the conservative quantities, conjugates of the scale variables through the action, which find their origin in the symmetries of the ''scale-space.'' We thus found in a geometric way and recover the expression for the covariant derivative of gauge theory. Adding the requirement that under the scale transformations the fermion multiplets and the boson fields transform such that the derived Lagrangian remains invariant, we obtain gauge theories as a consequence of scale symmetries issued from a geometric space-time description.
Star democracy in open string field theory
NASA Astrophysics Data System (ADS)
Maccaferri, Carlo; Mamone, Davide
2003-09-01
We study three types of star products in SFT: the ghosts, the twisted ghosts and the matter. We find that their Neumann coefficients are related to each other in a compact way which includes the Gross-Jevicki relation between matter and ghost sector: we explicitly show that the same relation, with a minus sign, holds for the twisted and nontwisted ghosts (which are different but define the same solution). In agreement with this, we prove that matter and twisted ghost coefficients just differ by a minus sign. As a consistency check, we also compute the spectrum of the twisted ghost vertices from conformal field theory and, using equality of twisted and reduced slivers, we derive the spectrum of the non twisted ghost star.
Machine Learning for Dynamical Mean Field Theory
NASA Astrophysics Data System (ADS)
Arsenault, Louis-Francois; Lopez-Bezanilla, Alejandro; von Lilienfeld, O. Anatole; Littlewood, P. B.; Millis, Andy
2014-03-01
Machine Learning (ML), an approach that infers new results from accumulated knowledge, is in use for a variety of tasks ranging from face and voice recognition to internet searching and has recently been gaining increasing importance in chemistry and physics. In this talk, we investigate the possibility of using ML to solve the equations of dynamical mean field theory which otherwise requires the (numerically very expensive) solution of a quantum impurity model. Our ML scheme requires the relation between two functions: the hybridization function describing the bare (local) electronic structure of a material and the self-energy describing the many body physics. We discuss the parameterization of the two functions for the exact diagonalization solver and present examples, beginning with the Anderson Impurity model with a fixed bath density of states, demonstrating the advantages and the pitfalls of the method. DOE contract DE-AC02-06CH11357.
Effective field theory analysis of Higgs naturalness
Bar-Shalom, Shaouly; Soni, Amarjit; Wudka, Jose
2015-07-20
Assuming the presence of physics beyond the Standard Model ( SM) with a characteristic scale M ~ O (10) TeV, we investigate the naturalness of the Higgs sector at scales below M using an effective field theory (EFT) approach. We obtain the leading 1 -loop EFT contributions to the Higgs mass with a Wilsonian-like hard cutoff, and determine t he constraints on the corresponding operator coefficients for these effects to alleviate the little hierarchy problem up to the scale of the effective action Λ < M , a condition we denote by “EFT-naturalness”. We also determine the types of physics that can lead to EFT-naturalness and show that these types of new physics are best probed in vector-boson and multiple-Higgs production. The current experimental constraints on these coefficients are also discussed.
Effective field theory for cold atoms
Hammer, H.-W.
2005-05-06
Effective Field Theory (EFT) provides a powerful framework that exploits a separation of scales in physical systems to perform systematically improvable, model-independent calculations. Particularly interesting are few-body systems with short-range interactions and large two-body scattering length. Such systems display remarkable universal features. In systems with more than two particles, a three-body force with limit cycle behavior is required for consistent renormalization already at leading order. We will review this EFT and some of its applications in the physics of cold atoms. Recent extensions of this approach to the four-body system and N-boson droplets in two spatial dimensions will also be discussed.
Matrix product states for gauge field theories.
Buyens, Boye; Haegeman, Jutho; Van Acoleyen, Karel; Verschelde, Henri; Verstraete, Frank
2014-08-29
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study (1+1)-dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground-state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study full quantum nonequilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field.
Non-rigid molecular group theory and its applications
Balasubramanian, K.
1982-06-01
The use of generalized wreath product groups as representations of symmetry groups of nonrigid molecules is considered. Generating function techniques are outlined for nuclear spin statistics and character tables of the symmetry groups of nonrigid molecules. Several applications of nonrigid molecular group theory to NMR spectroscopy, rovibronic splitting and nuclear spin statistics of nonrigid molecules, molecular beam deflection and electric resonance experiments of weakly bound Van der Waal complexes, isomerization processes, configuration interaction calculations and the symmetry of crystals with structural distortions are described. 81 references.
The $\\hbar$ Expansion in Quantum Field Theory
Brodsky, Stanley J.; Hoyer, Paul; /Southern Denmark U., CP3-Origins /Helsinki U. /Helsinki Inst. of Phys.
2010-10-27
We show how expansions in powers of Planck's constant {h_bar} = h = 2{pi} can give new insights into perturbative and nonperturbative properties of quantum field theories. Since {h_bar} is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the {h_bar} expansion depends on the scheme; i.e., different expansions are obtained depending on which quantities (momenta, couplings and masses) are assumed to be independent of {h_bar}. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be independent of {h_bar}, then each loop in perturbation theory brings a factor of {h_bar}. In the case of quantum electrodynamics, this scheme implies that the classical charge e, as well as the fine structure constant are linear in {h_bar}. The connection between the number of loops and factors of {h_bar} is more subtle for bound states since the binding energies and bound-state momenta themselves scale with {h_bar}. The {h_bar} expansion allows one to identify equal-time relativistic bound states in QED and QCD which are of lowest order in {h_bar} and transform dynamically under Lorentz boosts. The possibility to use retarded propagators at the Born level gives valence-like wave-functions which implicitly describe the sea constituents of the bound states normally present in its Fock state representation.
Quantum field theory in non-integer dimensions
Eyink, G.L.
1987-01-01
In a 1973 paper entitled Quantum Field-Theory Models in Less Than 4 Dimensions, Kenneth G. Wilson studied field-theories for spacetime dimension d between 2 and 4. With unconventional renormalizations, these models were found to have non-Gaussian ultraviolet renormalization group fixed points. Wilson's method was perturbative dimensional regularization: the Feynman-graph integrals were analytically continued to non-integer d. His work left open the question of the nonperturbative existence of the models. Since that landmark paper, Yuval Gefen, Amnon Aharony and Benoit B. Mandelbrot have shown that Ising spin models on fractal lattices have critical properties like those predicted for non-integer dimensions by the analytic continuation, or {epsilon}-expansion method. This work shows that fractal lattices and continua provide also a nonperturbative definition of field-theories in non-integer dimensions. The fractal point-sets employed are the Sierpinski carpets and their higher-dimensional generalizations. This class of point-sets has a tunable dimension which allows the approach to four from below. Furthermore, the carpets have discrete groups of scale or dilation invariances and infinite order of ramification. A class of scalar field models are defined on these sets which should reduce to the standard models when d {nearrow}4. The propagator for these models is given by a proper-time or heat-kernel representation. For this propagator, reflection-positivity is established, a general scaling law is conjectured (and established in a special case), and the perturbative renormalizability shown to be governed by the spectral dimensionality. Scalar models with another choice of propagator, the hierarchical propagator, are studied by rigorous renormalization-group methods.
Neural field theory with variance dynamics.
Robinson, P A
2013-06-01
Previous neural field models have mostly been concerned with prediction of mean neural activity and with second order quantities such as its variance, but without feedback of second order quantities on the dynamics. Here the effects of feedback of the variance on the steady states and adiabatic dynamics of neural systems are calculated using linear neural field theory to estimate the neural voltage variance, then including this quantity in the total variance parameter of the nonlinear firing rate-voltage response function, and thus into determination of the fixed points and the variance itself. The general results further clarify the limits of validity of approaches with and without inclusion of variance dynamics. Specific applications show that stability against a saddle-node bifurcation is reduced in a purely cortical system, but can be either increased or decreased in the corticothalamic case, depending on the initial state. Estimates of critical variance scalings near saddle-node bifurcation are also found, including physiologically based normalizations and new scalings for mean firing rate and the position of the bifurcation.
Propagation in polymer parameterised field theory
NASA Astrophysics Data System (ADS)
Varadarajan, Madhavan
2017-01-01
The Hamiltonian constraint operator in loop quantum gravity acts ultralocally. Smolin has argued that this ultralocality seems incompatible with the existence of a quantum dynamics which propagates perturbations between macroscopically seperated regions of quantum geometry. We present evidence to the contrary within an LQG type ‘polymer’ quantization of two dimensional parameterised field theory (PFT). PFT is a generally covariant reformulation of free field propagation on flat spacetime. We show explicitly that while, as in LQG, the Hamiltonian constraint operator in PFT acts ultralocally, states in the joint kernel of the Hamiltonian and diffeomorphism constraints of PFT necessarily describe propagation effects. The particular structure of the finite triangulation Hamiltonian constraint operator plays a crucial role, as does the necessity of imposing (the continuum limit of) its kinematic adjoint as a constraint. Propagation is seen as a property encoded by physical states in the kernel of the constraints rather than that of repeated actions of the finite triangulation Hamiltonian constraint on kinematic states. The analysis yields robust structural lessons for putative constructions of the Hamiltonian constraint in LQG for which ultralocal action co-exists with a description of propagation effects by physical states.
Topological field theory of dynamical systems
Ovchinnikov, Igor V.
2012-09-15
Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken Q-symmetry, chaotic models with Q-symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with Q-symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches, etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the 'edge of chaos.' Goldstone theorem stands behind spatio-temporal self-similarity of Q-broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions, etc. Other fundamental differences of Q-broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. Q-symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed.
Topological field theory of dynamical systems.
Ovchinnikov, Igor V
2012-09-01
Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken Q-symmetry, chaotic models with Q-symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with Q-symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches, etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the "edge of chaos." Goldstone theorem stands behind spatio-temporal self-similarity of Q-broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions, etc. Other fundamental differences of Q-broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. Q-symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed.
Topological field theory of dynamical systems
NASA Astrophysics Data System (ADS)
Ovchinnikov, Igor V.
2012-09-01
Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken Q-symmetry, chaotic models with Q-symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with Q-symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches, etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the "edge of chaos." Goldstone theorem stands behind spatio-temporal self-similarity of Q-broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions, etc. Other fundamental differences of Q-broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. Q-symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed.
How Group Dynamics Research Can Inform the Theory and Practice of Postsecondary Small Group Learning
ERIC Educational Resources Information Center
Sweet, Michael; Michaelsen, Larry K.
2007-01-01
After a brief review of integrative small group learning models that have appeared in the educational psychology literature, this article then looks into the group dynamics literature and describes one of that field's most well-documented findings: that interactions among group members change somewhat predictably over time. How theorists from…
The Physical Renormalization of Quantum Field Theories
Binger, Michael William.; /Stanford U., Phys. Dept. /SLAC
2007-02-20
The profound revolutions in particle physics likely to emerge from current and future experiments motivates an improved understanding of the precise predictions of the Standard Model and new physics models. Higher order predictions in quantum field theories inevitably requires the renormalization procedure, which makes sensible predictions out of the naively divergent results of perturbation theory. Thus, a robust understanding of renormalization is crucial for identifying and interpreting the possible discovery of new physics. The results of this thesis represent a broad set of investigations in to the nature of renormalization. The author begins by motivating a more physical approach to renormalization based on gauge-invariant Green's functions. The resulting effective charges are first applied to gauge coupling unification. This approach provides an elegant formalism for understanding all threshold corrections, and the gauge couplings unify in a more physical manner compared to the usual methods. Next, the gauge-invariant three-gluon vertex is studied in detail, revealing an interesting and rich structure. The effective coupling for the three-gluon vertex, {alpha}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}), depends on three momentum scales and gives rise to an effective scale Q{sub eff}{sup 2}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}) which governs the (sometimes surprising) behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudo-threshold structure. The pinch-technique effective charge is also calculated to two-loops and several applications are discussed. The Higgs boson mass in Split Supersymmetry is calculated to two-loops, including all one-loop threshold effects, leading to a downward shift in the Higgs mass of a few GeV. Finally, the author discusses some ideas regarding the overall structure of perturbation theory. This thesis lays the foundation for a comprehensive multi
Halo nuclei interactions using effective field theory
NASA Astrophysics Data System (ADS)
Fernando, Nippalage Lakma Kaushalya
Effective field theory (EFT) provides a framework to exploit separation of scales in the physical system in order to perform systematic model-independent calculations. There has been significant interest in applying the methods of EFT to halo nuclei. Using halo effective field theory, I provide a model-independent calculation of the radiative neutron capture on lithium-7 over an energy range where the contribution from the 3+ resonance becomes important. This reaction initiate the sequence in the carbon-nitrogen-oxygen (CNO) cycle in the inhomogeneous BBN models, and determine the amount of heavy element production from its reaction rate. One finds that a satisfactory description of the capture reaction, in the present single-particle approximation, suggests the use of a resonance width about three times larger than the experimental value. Power counting arguments that establish a hierarchy for the electromagnetic one- and two-body currents is also presented. The neutron capture of Lithium7 calculation has direct impact on the proton capture on beryllium7 which plays an important role in the neutrino experiments studying physics beyond the Standard Model of particle physics. As a further study of halo nuclei interactions, the cross section of radiative capture of a neutron by carbon-14 is calculated by considering the dominant contribution from electric dipole transition. This is also a part of the CNO cycle and as the slowest reaction in the chain it limits the flow of the production of heavier nuclei A > 14. The cross section is expressed in terms of the elastic scattering parameters of an effective range expansion. Contributions from both the resonant and non-resonant interactions are calculated. Significant interferences between these leads to a capture contribution that deviates from a simple Breit-Wigner resonance form. Using EFT, I present electromagnetic form factors of several halo nuclei. The magnetic dipole moment and the charge radii of carbon-15
Does there exist a sensible quantum theory of an ``algebra-valued'' scalar field\\?
NASA Astrophysics Data System (ADS)
Anco, Stephen C.; Wald, Robert M.
1989-04-01
Consider a scalar field φ in Minkowski spacetime, but let φ be valued in an associative, commutative algebra openA rather than openR. One may view the resulting theory as describing a collection of coupled real scalar fields. At the classical level, theories of this type are completely well behaved and have a global symmetry group which is a nontrivial enlargement of the Poincaré group. (They are analogs of the new class of gauge theories for massless spin-2 fields found recently by one of us, whose gauge group is a nontrivial enlargement of the usual diffeomorphism group.) We investigate the quantization of such scalar field theories here by studying the case of a λφ4 field, with φ valued in the two-dimensional algebra generated by an identity element e and a nilpotent element v satisfying v2=0. The Coleman-Mandula theorem, which states that the symmetry group of a nontrivial quantum field theory cannot be a nontrivial enlargement of the Poincaré group, is evaded here because the finite ``extra'' symmetries of the classical theory fail to be implemented in the quantum theory by unitary operators and the infinitesimal symmetries (which can be represented in the quantum theory by quadratic forms) connect the one-particle Hilbert space to multiparticle states. Nevertheless, we find that the conventional Feynman rules for this theory lead to vacuum decay at the tree level and fail to yield a well-defined S matrix. Some alternative approaches are investigated, but these also appear to fail. Thus, although the classical theory is perfectly well behaved, it seems that there does not exist a sensible quantum theory of an algebra-valued scalar field.
Renormalization Group Theory of Bolgiano Scaling in Boussinesq Turbulence
NASA Technical Reports Server (NTRS)
Rubinstein, Robert
1994-01-01
Bolgiano scaling in Boussinesq turbulence is analyzed using the Yakhot-Orszag renormalization group. For this purpose, an isotropic model is introduced. Scaling exponents are calculated by forcing the temperature equation so that the temperature variance flux is constant in the inertial range. Universal amplitudes associated with the scaling laws are computed by expanding about a logarithmic theory. Connections between this formalism and the direct interaction approximation are discussed. It is suggested that the Yakhot-Orszag theory yields a lowest order approximate solution of a regularized direct interaction approximation which can be corrected by a simple iterative procedure.
Wilsonian matching of effective field theory with underlying QCD
Harada, Masayasu; Yamawaki, Koichi
2001-07-01
We propose a novel way of matching effective field theory with the underlying QCD in the sense of a Wilsonian renormalization group equation (RGE). We derive Wilsonian matching conditions between current correlators obtained by the operator product expansion in QCD and those by the hidden local symmetry (HLS) model. This determines without much ambiguity the bare parameters of the HLS at the cutoff scale in terms of the QCD parameters. Physical quantities for the {pi} and {rho} system are calculated by the Wilsonian RGE{close_quote}s from the bare parameters in remarkable agreement with the experiment.
Gravitational consequences of modern field theories
NASA Technical Reports Server (NTRS)
Horowitz, Gary T.
1989-01-01
Some gravitational consequences of certain extensions of Einstein's general theory of relativity are discussed. These theories are not alternative theories of gravity in the usual sense. It is assumed that general relativity is the appropriate description of all gravitational phenomena which were observed to date.
Quarkonium hybrids with nonrelativistic effective field theories
NASA Astrophysics Data System (ADS)
Berwein, Matthias; Brambilla, Nora; Tarrús Castellà, Jaume; Vairo, Antonio
2015-12-01
We construct a nonrelativistic effective field theory description of heavy quarkonium hybrids from QCD. We identify the symmetries of the system made of a heavy quark, a heavy antiquark, and glue in the static limit. Corrections to this limit can be obtained order by order in an expansion in the inverse of the mass m of the heavy quark. At order 1 /m in the expansion, we obtain, at the level of potential nonrelativistic QCD, a system of coupled Schrödinger equations that describes hybrid spin-symmetry multiplets, including the mixing of different static energies into the hybrid states, an effect known as Λ doubling in molecular physics. In the short distance, the static potentials depend on two nonperturbative parameters, the gluelump mass and the quadratic slope, which can be determined from lattice calculations. We adopt a renormalon subtraction scheme for the calculation of the perturbative part of the potential. We numerically solve the coupled Schrödinger equations and obtain the masses for the lowest lying spin-symmetry multiplets for c c ¯, b c ¯, and b b ¯ hybrids. The Λ -doubling effect breaks the degeneracy between opposite-parity spin-symmetry multiplets and lowers the mass of the multiplets that get mixed contributions of different static energies. We compare our findings to the experimental data, direct lattice computations, and sum rule calculations, and discuss the relation to the Born-Oppenheimer approximation.
Quantum Field Theory of Kosterlitz-Thouless Phase Transitions.
NASA Astrophysics Data System (ADS)
Ogilvie, Michael Charles
1980-12-01
A general quantum field-theoretic formalism for the study of Kosterlitz-Thouless phase transition is developed and applied to several models. The structure of the free, massless scalar field is discussed, making explicit its connection with the Gaussian model. The close connection of the spin-wave and vortex operators with two-dimensional fermion-boson equivalences is stressed. The critical behavior of the planar model is reviewed, using field-theoretic methods applied to the sine-Gordon model. The Kosterlitz -Thouless phase transition in two-dimensional dislocation -mediated melting is studied using a vector generalization of the sine-Gordon model. Recent second-order renormalization group calculations are confirmed, and the issue of universal third-order corrections is discussed. It is shown that the Gross-Neveu model can be interpreted as a massive theory associated with a Kosterlitz-Thouless critical point. Finally, the Ising and Baxter models are studied using the methods developed here. It is shown that the vortex and spin-wave excitations in the Ising model conspire to produce a free, massive Majorana fermion field theory in the continuum limit. The formalism is then extended to the Baxter model. Recent results on the Baxter and Ashkin-Teller models are rederived and extended.
Field Theories from the Relativistic Law of Motion
NASA Astrophysics Data System (ADS)
Singh, Parampreet; Dadhich, Naresh
From the relativistic law of motion we attempt to deduce the field theories corresponding to the force law being linear and quadratic in four-velocity of the particle. The linear law leads to the vector gauge theory which could be the Abelian Maxwell electrodynamics or the non-Abelian Yang-Mills theory. On the other hand, the quadratic law demands space-time metric as its potential which is equivalent to demanding the principle of equivalence. It leads to the tensor theory of gravitational field - general relativity. It is remarkable that a purely dynamical property of the force law leads uniquely to the corresponding field theories.
A Geometrically Nonlinear Phase Field Theory of Brittle Fracture
2014-10-01
A Geometrically Nonlinear Phase Field Theory of Brittle Fracture by JD Clayton and J Knap ARL-RP-0511 October 2014...21005-5069 ARL-RP-0511 October 2014 A Geometrically Nonlinear Phase Field Theory of Brittle Fracture JD Clayton and J Knap Weapons and...Nonlinear Phase Field Theory of Brittle Fracture 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) JD Clayton
Generally covariant vs. gauge structure for conformal field theories
Campigotto, M.; Fatibene, L.
2015-11-15
We introduce the natural lift of spacetime diffeomorphisms for conformal gravity and discuss the physical equivalence between the natural and gauge natural structure of the theory. Accordingly, we argue that conformal transformations must be introduced as gauge transformations (affecting fields but not spacetime point) and then discuss special structures implied by the splitting of the conformal group. -- Highlights: •Both a natural and a gauge natural structure for conformal gravity are defined. •Global properties and natural lift of spacetime transformations are described. •The possible definitions of physical state are considered and discussed. •The gauge natural theory has less physical states than the corresponding natural one. •The dynamics forces to prefer the gauge natural structure over the natural one.
Membrane stress profiles from self-consistent field theory
NASA Astrophysics Data System (ADS)
Ting, Christina L.; Müller, Marcus
2017-03-01
Using self-consistent field theory (SCFT), we develop an accurate, local expression for the stress profiles in membranes and soft matter interfaces, in general. The bond stresses are expressed in terms of pre-computed chain propagators, which are used to describe the statistical weight of the molecules and therefore require minimal additional calculations. In addition, we overcome the resolution limit of the molecular bond length by including the Irving and Kirkwood bond assignment and recover a constant normal stress profile across an interface. Using this theory, we find that the membrane lateral stress profile contains repulsive (positive) stresses in the regions of the head and tail groups, and attractive (negative) stresses near the hydrophobic/hydrophilic interface. We also verify that the zeroth and first moments of the stress profile correspond to the thermodynamic tension and product of the bending modulus and the spontaneous curvature, respectively.
Group psychotherapy and neuro-plasticity: an attachment theory perspective.
Flores, Philip J
2010-10-01
This article selectively highlights relevant areas of neuroscience research which have direct application for attachment theory and group psychotherapy. Emerging evidence from the neurosciences is revealing that the developing brain of the infant, sculpted by the earliest attachment relationships, continues to be malleable in adulthood and can be profoundly influenced by ongoing relationships throughout one's lifespan. Advances in the neurosciences are also supporting the idea that strong attachment bonds and external interpersonal interactions that arise within the context of these attachments are registered as a person's neurophysiology and neurobiology. Attachment theory in particular provides a common language and conceptual framework from which the contributions from the neurosciences can be made applicable to group psychotherapy.
Affine reflection groups for tiling applications: Knot theory and DNA
NASA Astrophysics Data System (ADS)
Bodner, M.; Patera, J.; Peterson, M.
2012-01-01
We present in this paper some non-conventional applications of affine Weyl groups Waff of rank 2, the symmetry group of the tiling/lattice. We first develop and present the tools for applications requiring tilings of a real Euclidean plane {R}^2. We then elucidate the equivalence of these tilings with 2D projections of knots. The resulting mathematical structure provides a framework within which is encompassed recent work utilizing knot theory for modeling the structure and function of genetic molecules, specifically the action of particular enzymes in altering the topology of DNA in site-specific recombination.
Differential cohomology and locally covariant quantum field theory
NASA Astrophysics Data System (ADS)
Becker, Christian; Schenkel, Alexander; Szabo, Richard J.
We study differential cohomology on categories of globally hyperbolic Lorentzian manifolds. The Lorentzian metric allows us to define a natural transformation whose kernel generalizes Maxwell's equations and fits into a restriction of the fundamental exact sequences of differential cohomology. We consider smooth Pontryagin duals of differential cohomology groups, which are subgroups of the character groups. We prove that these groups fit into smooth duals of the fundamental exact sequences of differential cohomology and equip them with a natural presymplectic structure derived from a generalized Maxwell Lagrangian. The resulting presymplectic Abelian groups are quantized using the CCR-functor, which yields a covariant functor from our categories of globally hyperbolic Lorentzian manifolds to the category of C∗-algebras. We prove that this functor satisfies the causality and time-slice axioms of locally covariant quantum field theory, but that it violates the locality axiom. We show that this violation is precisely due to the fact that our functor has topological subfunctors describing the Pontryagin duals of certain singular cohomology groups. As a byproduct, we develop a Fréchet-Lie group structure on differential cohomology groups.
Translational symmetry breaking in field theories and the cosmological constant
NASA Astrophysics Data System (ADS)
Evans, Nick; Morris, Tim R.; Scott, Marc
2016-01-01
We argue, at a very basic effective field theory level, that higher dimension operators in scalar theories that break symmetries at scales close to their ultraviolet completion cutoff include terms that favor the breaking of translation (Lorentz) invariance, potentially resulting in striped, checkerboard or general crystal-like phases. Such descriptions can be thought of as the effective low energy description of QCD-like gauge theories near their strong coupling scale where terms involving higher dimension operators are generated. Our low energy theory consists of scalar fields describing operators such as q ¯q and q ¯F(2 n )q . Such scalars can have kinetic mixing terms that generate effective momentum dependent contributions to the mass matrix. We show that these can destabilize the translationally invariant vacuum. It is possible that in some real gauge theory such operators could become sufficiently dominant to realize such phases, and it would be interesting to look for them in lattice simulations. We present a holographic model of the same phenomena which includes renormalization group running. A key phenomenological motive to look at such states is recent work that shows that the nonlinear response in R2 gravity to such short-range fluctuations can mimic a cosmological constant. Intriguingly in a cosmology with such a Starobinsky inflation term, to generate the observed value of the present day acceleration would require stripes at the electroweak scale. Unfortunately, low energy phenomenological constraints on Lorentz violation in the electron-photon system appear to strongly rule out any such possibility outside of a disconnected dark sector.
Application of Group Theory to Some Problems in Atomic Physics.
NASA Astrophysics Data System (ADS)
Suskin, Mark Albert
This work comprises three problems, each of which lends itself to investigation via the theory of groups and group representations. The first problem is to complete a set of operators used in the fitting of atomic energy levels of atoms whose ground configuration is f ^ 3. The role of group theory in the labelling of these operators and in their construction is explained. Values of parameters associated with a subset of the operators are also calculated via their group labels. The second problem is to explain the term inversion that occurs between states of the configuration of two equivalent electrons and certain of the states of the half-filled shell. This leads to generalizations that make it possible to investigate correspondences between matrix elements of effective operators taken between states of other configurations besides the two mentioned. This is made possible through the notion of quasispin. The third problem is the construction of recoupling coefficients for groups other than SO(3). Questions of phase convention and Kronecker-product multiplicities are taken up. Several methods of calculation are given and their relative advantages discussed. Tables of values of the calculated 6-j symbols are provided.
Topics in topological and holomorphic quantum field theory
NASA Astrophysics Data System (ADS)
Vyas, Ketan
We investigate topological quantum field theories (TQFTs) in two, three, and four dimensions, as well as holomorphic quantum field theories (HQFTs) in four dimensions. After a brief overview of the two-dimensional (gauged) A and B models and the corresponding the category of branes, we construct analogous three-dimensional (gauged) A and B models and discuss the two-category of boundary conditions. Compactification allows us to identify the category of line operators in the three-dimensional A and B models with the category of branes in the corresponding two-dimensional A and B models. Furthermore, we use compactification to identify the two-category of surface operators in the four-dimensional GL theory at t = 1 and t = i with the two-category of boundary conditions in the corresponding three-dimensional A and B model, respectively. We construct a four-dimensional HQFT related to N = 1 supersymmetric quantum chromodynamics (SQCD) with gauge group SU(2) and two flavors, as well as a four-dimensional HQFT related to the Seiberg dual chiral model. On closed K ̈ahler surfaces with h^(2,0) > 0, we show that the correlation functions of holomorphic SQCD formally compute certain Donaldson invariants. For simply-connected elliptic surfaces (and their blow-ups), we show that the corresponding correlation functions in the holomorphic chiral model explicitly compute these Donaldson invariants.
Group-theoretic relations for amplitudes in gauge theories with orthogonal and symplectic groups
NASA Astrophysics Data System (ADS)
Huang, Jia-Hui
2017-01-01
It is important to find nontrivial constraint relations for color-ordered amplitudes in gauge theories. In the past several years, a pure group-theoretic iterative method has been proposed for deriving linear constraints on color-ordered amplitudes in S U (N ) gauge theories. In this paper, we use the same method to derive linear constraints on four-point gluon amplitudes in S O (N ) and S p (2 N ) gauge theories. These constraints are derived up to four-loop order. It is found that there are n =1 , 6, 10, 13, 16 constraint relations at L =0 , 1, 2, 3, 4 loop orders in both S O (N ) and S p (2 N ) cases. Correspondingly, there are 2,3,5,8, and 11 independent four-point color-ordered amplitudes at L =0 , 1, 2, 3, 4 loop orders in both theories.
Effective field theories for muonic hydrogen
NASA Astrophysics Data System (ADS)
Peset, Clara
2017-03-01
Experimental measurements of muonic hydrogen bound states have recently started to take place and provide a powerful setting in which to study the properties of QCD. We profit from the power of effective field theories (EFTs) to provide a theoretical framework in which to study muonic hydrogen in a model independent fashion. In particular, we compute expressions for the Lamb shift and the hyperfine splitting. These expressions include the leading logarithmic O(mμα6) terms, as well as the leading {\\cal O}≤ft( {{m_μ }{α ^5}{{m_μ ^2} \\over {Λ {{QCD}}^2}}} \\right) hadronic effects. Most remarkably, our analyses include the determination of the spin-dependent and spin-independent structure functions of the forward virtualphoton Compton tensor of the proton to O(p3) in HBET and including the Delta particle. Using these results we obtain the leading hadronic contributions to the Wilson coeffcients of the lepton-proton four fermion operators in NRQED. The spin-independent coeffcient yields a pure prediction for the two-photon exchange contribution to the muonic hydrogen Lamb shift, which is the main source of uncertainty in our computation. The spindependent coeffcient yields the prediction of the hyperfine splitting. The use of EFTs crucially helps us organizing the computation, in such a way that we can clearly address the parametric accuracy of our result. Furthermore, we review in the context of NRQED all the contributions to the energy shift of O(mμα5, as well as those that scale like mrα6× logarithms.
Variational principles for multisymplectic second-order classical field theories
NASA Astrophysics Data System (ADS)
Prieto-Martínez, Pedro Daniel; Román-Roy, Narciso
2015-06-01
We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this unified framework.
Field theory on R× S 3 topology. VI: Gravitation
NASA Astrophysics Data System (ADS)
Carmeli, M.; Malin, S.
1987-04-01
We extend to curved space-time the field theory on R×S3 topology in which field equations were obtained for scalar particles, spin one-half particles, the electromagnetic field of magnetic moments, an SU2 gauge theory, and a Schrödinger-type equation, as compared to ordinary field equations that are formulated on a Minkowskian metric. The theory obtained is an angular-momentum representation of gravitation. Gravitational field equations are presented and compared to the Einstein field equations, and the mathematical and physical similarity and differences between them are pointed out. The problem of motion is discussed, and the equations of motion of a rigid body are developed and given explicitly. One result which is worth emphazing is that while general relativity theory yields Newton's law of motion in the lowest approximation, our theory gives Euler's equations of motion for a rigid body in its lowest approximation.
Group Decisions in Biodiversity Conservation: Implications from Game Theory
Frank, David M.; Sarkar, Sahotra
2010-01-01
Background Decision analysis and game theory [1], [2] have proved useful tools in various biodiversity conservation planning and modeling contexts [3]–[5]. This paper shows how game theory may be used to inform group decisions in biodiversity conservation scenarios by modeling conflicts between stakeholders to identify Pareto–inefficient Nash equilibria. These are cases in which each agent pursuing individual self–interest leads to a worse outcome for all, relative to other feasible outcomes. Three case studies from biodiversity conservation contexts showing this feature are modeled to demonstrate how game–theoretical representation can inform group decision-making. Methodology and Principal Findings The mathematical theory of games is used to model three biodiversity conservation scenarios with Pareto–inefficient Nash equilibria: (i) a two–agent case involving wild dogs in South Africa; (ii) a three–agent raptor and grouse conservation scenario from the United Kingdom; and (iii) an n–agent fish and coral conservation scenario from the Philippines. In each case there is reason to believe that traditional mechanism–design solutions that appeal to material incentives may be inadequate, and the game–theoretical analysis recommends a resumption of further deliberation between agents and the initiation of trust—and confidence—building measures. Conclusions and Significance Game theory can and should be used as a normative tool in biodiversity conservation contexts: identifying scenarios with Pareto–inefficient Nash equilibria enables constructive action in order to achieve (closer to) optimal conservation outcomes, whether by policy solutions based on mechanism design or otherwise. However, there is mounting evidence [6] that formal mechanism–design solutions may backfire in certain cases. Such scenarios demand a return to group deliberation and the creation of reciprocal relationships of trust. PMID:20523732
The State of the Field: Interdisciplinary Theory
ERIC Educational Resources Information Center
Newell, William H.
2013-01-01
This chronological overview of the development of interdisciplinary theory starts with the pre-cursors of theory: the development and elaboration of the definition of interdisciplinary studies, influential but problematic images of interdisciplinary studies proposed by Donald Campbell and Erich Jantsch, and best practices in interdisciplinary…
Exploring Group Cohesion in a Higher Education Field Experience
ERIC Educational Resources Information Center
Malcarne, Brian Keith
2012-01-01
The purpose of this study was to gain understanding into the experience of group cohesion for university students participating in an academic field experience. A mixed methods approach was used following a two-phase, sequential research design to help provide a more complete explanation of how group cohesion was impacted by the field experience.…
Parastatistics and conformal field theories in two dimensions
NASA Astrophysics Data System (ADS)
Mansouri, Freydoon; Wu, Xizeng
1989-04-01
The relation between parafermion field theories of order Q and the corresponding fermion field theories with SO(Q) symmetry is studied. It is shown that these theories are related but not identical. The explicit relation between the states and the observables of the two classes of theories are given without using the Klein transformations. The formalism is applied to the free conformally invariant parafermion theories in two dimensions. Their Virasoro algebra and SO(N) Kac-Moody algebra are given. The equivalence of their canonical form of the energy-momentum tensor with the Sugawara-Sommerfield form is also elucidated.
Towards a double field theory on para-Hermitian manifolds
NASA Astrophysics Data System (ADS)
Vaisman, Izu
2013-12-01
In a previous paper, we have shown that the geometry of double field theory has a natural interpretation on flat para-Kähler manifolds. In this paper, we show that the same geometric constructions can be made on any para-Hermitian manifold. The field is interpreted as a compatible (pseudo-)Riemannian metric. The tangent bundle of the manifold has a natural, metric-compatible bracket that extends the C-bracket of double field theory. In the para-Kähler case, this bracket is equal to the sum of the Courant brackets of the two Lagrangian foliations of the manifold. Then, we define a canonical connection and an action of the field that correspond to similar objects of double field theory. Another section is devoted to the Marsden-Weinstein reduction in double field theory on para-Hermitian manifolds. Finally, we give examples of fields on some well-known para-Hermitian manifolds.
Towards a double field theory on para-Hermitian manifolds
Vaisman, Izu
2013-12-15
In a previous paper, we have shown that the geometry of double field theory has a natural interpretation on flat para-Kähler manifolds. In this paper, we show that the same geometric constructions can be made on any para-Hermitian manifold. The field is interpreted as a compatible (pseudo-)Riemannian metric. The tangent bundle of the manifold has a natural, metric-compatible bracket that extends the C-bracket of double field theory. In the para-Kähler case, this bracket is equal to the sum of the Courant brackets of the two Lagrangian foliations of the manifold. Then, we define a canonical connection and an action of the field that correspond to similar objects of double field theory. Another section is devoted to the Marsden-Weinstein reduction in double field theory on para-Hermitian manifolds. Finally, we give examples of fields on some well-known para-Hermitian manifolds.
Wick rotation for quantum field theories on degenerate Moyal space(-time)
Grosse, Harald; Lechner, Gandalf; Ludwig, Thomas; Verch, Rainer
2013-02-15
In this paper the connection between quantum field theories on flat noncommutative space(-times) in Euclidean and Lorentzian signature is studied for the case that time is still commutative. By making use of the algebraic framework of quantum field theory and an analytic continuation of the symmetry groups which are compatible with the structure of Moyal space, a general correspondence between field theories on Euclidean space satisfying a time zero condition and quantum field theories on Moyal Minkowski space is presented ('Wick rotation'). It is then shown that field theories transferred to Moyal space(-time) by Rieffel deformation and warped convolution fit into this framework, and that the processes of Wick rotation and deformation commute.
Quantum field theory on toroidal topology: Algebraic structure and applications
NASA Astrophysics Data System (ADS)
Khanna, F. C.; Malbouisson, A. P. C.; Malbouisson, J. M. C.; Santana, A. E.
2014-05-01
The development of quantum theory on a torus has a long history, and can be traced back to the 1920s, with the attempts by Nordström, Kaluza and Klein to define a fourth spatial dimension with a finite size, being curved in the form of a torus, such that Einstein and Maxwell equations would be unified. Many developments were carried out considering cosmological problems in association with particle physics, leading to methods that are useful for areas of physics, in which size effects play an important role. This interest in finite size effect systems has been increasing rapidly over the last decades, due principally to experimental improvements. In this review, the foundations of compactified quantum field theory on a torus are presented in a unified way, in order to consider applications in particle and condensed matter physics. The theory on a torus ΓDd=(S1)d×RD-d is developed from a Lie-group representation and c*c*-algebra formalisms. As a first application, the quantum field theory at finite temperature, in its real- and imaginary-time versions, is addressed by focusing on its topological structure, the torus Γ41. The toroidal quantum-field theory provides the basis for a consistent approach of spontaneous symmetry breaking driven by both temperature and spatial boundaries. Then the superconductivity in films, wires and grains are analyzed, leading to some results that are comparable with experiments. The Casimir effect is studied taking the electromagnetic and Dirac fields on a torus. In this case, the method of analysis is based on a generalized Bogoliubov transformation, that separates the Green function into two parts: one is associated with the empty space-time, while the other describes the impact of compactification. This provides a natural procedure for calculating the renormalized energy-momentum tensor. Self interacting four-fermion systems, described by the Gross-Neveu and Nambu-Jona-Lasinio models, are considered. Then finite size effects on
Challenging Gender Stereotypes: Theory of Mind and Peer Group Dynamics
Mulvey, Kelly Lynn; Rizzo, Michael T.; Killen, Melanie
2016-01-01
To investigate the social cognitive skills related to challenging gender stereotypes, children (N = 61, 3-6 years) evaluated a peer who challenged gender stereotypic norms held by the peer’s group. Participants with false belief theory of mind (FB ToM) competence were more likely than participants who did not have FB ToM to expect a peer to challenge the group’s stereotypes and propose that the group engage in a non-stereotypic activity. Further, participants with FB ToM rated challenging the peer group more positively. Participants without FB ToM did not differentiate between their own and the group’s evaluation of challenges to the group’s stereotypic norms, but those with ToM competence asserted that they would be more supportive of challenging the group norm than would the peer group. Results reveal the importance of social-cognitive competencies for recognizing the legitimacy of challenging stereotypes, and for understanding one’s own and other group perspectives. PMID:26395753
Stability in higher-derivative matter fields theories
NASA Astrophysics Data System (ADS)
Tretyakov, Petr V.
2016-09-01
We discuss possible instabilities in higher-derivative matter field theories. These theories have two free parameters β _1 and β _4. By using a dynamical system approach we explicitly demonstrate that for the stability of Minkowski space in an expanding universe we need the condition β _4<0. By using the quantum field theory approach we also find an additional restriction for the parameters, β _1>-1/3β _4, which is needed to avoid a tachyon-like instability.
GravitoMagnetic Field in Tensor-Vector-Scalar Theory
Exirifard, Qasem
2013-04-01
We study the gravitomagnetism in the TeVeS theory. We compute the gravitomagnetic field that a slow moving mass distribution produces in its Newtonian regime. We report that the consistency between the TeVeS gravitomagnetic field and that predicted by the Einstein-Hilbert theory leads to a relation between the vector and scalar coupling constants of the theory. We translate the Lunar Laser Ranging measurement's data into a constraint on the deviation from this relation.
Matter-enhanced transition probabilities in quantum field theory
Ishikawa, Kenzo Tobita, Yutaka
2014-05-15
The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincaré transformation. The ground state, vacuum, is singlet and one particle states are transformed as elements of irreducible representation of the group. The covariant one particles are momentum eigenstates expressed by plane waves and extended in space. Although the S-matrix defined with initial and final states of these states hold the symmetries and are applied to isolated states, out-going states for the amplitude of the event that they are detected at a finite-time interval T in experiments are expressed by microscopic states that they interact with, and are surrounded by matters in detectors and are not plane waves. These matter-induced effects modify the probabilities observed in realistic situations. The transition amplitudes and probabilities of the events are studied with the S-matrix, S[T], that satisfies the boundary condition at T. Using S[T], the finite-size corrections of the form of 1/T are found. The corrections to Fermi’s golden rule become larger than the original values in some situations for light particles. They break Lorentz invariance even in high energy region of short de Broglie wave lengths. -- Highlights: •S-matrix S[T] for the finite-time interval in relativistic field theory. •S[T] satisfies the boundary condition and gives correction of 1/T . •The large corrections for light particles breaks Lorentz invariance. •The corrections have implications to neutrino experiments.
ERIC Educational Resources Information Center
Terborg, James R.; And Others
In a longitudinal field experiment, 42 groups were assembled on the factors of individual ability and attitude similarity resulting in a 2 x 2 crossed ANOVA design. These groups then worked on six projects which spanned a three-month time period. For each project, measures of group performance and group cohesion were taken. Analyses showed that…
Effective field theory of broken spatial diffeomorphisms
Lin, Chunshan; Labun, Lance Z.
2016-03-17
We study the low energy effective theory describing gravity with broken spatial diffeomorphism invariance. In the unitary gauge, the Goldstone bosons associated with broken diffeomorphisms are eaten and the graviton becomes a massive spin-2 particle with 5 well-behaved degrees of freedom. In this gauge, the most general theory is built with the lowest dimension operators invariant under only temporal diffeomorphisms. Imposing the additional shift and SO(3) internal symmetries, we analyze the perturbations on a FRW background. At linear perturbation level, the observables of this theory are characterized by five parameters, including the usual cosmological parameters and one additional coupling constantmore » for the symmetry-breaking scalars. In the de Sitter and Minkowski limit, the three Goldstone bosons are supermassive and can be integrated out, leaving two massive tensor modes as the only propagating degrees of freedom. In conclusion, we discuss several examples relevant to theories of massive gravity.« less
Effective field theory of broken spatial diffeomorphisms
Lin, Chunshan; Labun, Lance Z.
2016-03-17
We study the low energy effective theory describing gravity with broken spatial diffeomorphism invariance. In the unitary gauge, the Goldstone bosons associated with broken diffeomorphisms are eaten and the graviton becomes a massive spin-2 particle with 5 well-behaved degrees of freedom. In this gauge, the most general theory is built with the lowest dimension operators invariant under only temporal diffeomorphisms. Imposing the additional shift and SO(3) internal symmetries, we analyze the perturbations on a FRW background. At linear perturbation level, the observables of this theory are characterized by five parameters, including the usual cosmological parameters and one additional coupling constant for the symmetry-breaking scalars. In the de Sitter and Minkowski limit, the three Goldstone bosons are supermassive and can be integrated out, leaving two massive tensor modes as the only propagating degrees of freedom. In conclusion, we discuss several examples relevant to theories of massive gravity.
Does there exist a sensible quantum theory of an ''algebra-valued'' scalar field
Anco, S.C.; Wald, R.M.
1989-04-15
Consider a scalar field phi in Minkowski spacetime, but let phi be valued in an associative, commutative algebra openA rather than openR. One may view the resulting theory as describing a collection of coupled real scalar fields. At the classical level, theories of this type are completely well behaved and have a global symmetry group which is a nontrivial enlargement of the Poincare group. (They are analogs of the new class of gauge theories for massless spin-2 fields found recently by one of us, whose gauge group is a nontrivial enlargement of the usual diffeomorphism group.) We investigate the quantization of such scalar field theories here by studying the case of a lambdaphi/sup 4/ field, with phi valued in the two-dimensional algebra generated by an identity element e and a nilpotent element v satisfying v/sup 2/ = 0. The Coleman-Mandula theorem, which states that the symmetry group of a nontrivial quantum field theory cannot be a nontrivial enlargement of the Poincare group, is evaded here because the finite ''extra'' symmetries of the classical theory fail to be implemented in the quantum theory by unitary operators and the infinitesimal symmetries (which can be represented in the quantum theory by quadratic forms) connect the one-particle Hilbert space to multiparticle states. Nevertheless, we find that the conventional Feynman rules for this theory lead to vacuum decay at the tree level and fail to yield a well-defined S matrix. Some alternative approaches are investigated, but these also appear to fail.
Mean-field theory for Bose-Hubbard model under a magnetic field
Oktel, M. Oe.; Tanatar, B.; Nita, M.
2007-01-15
We consider the superfluid-insulator transition for cold bosons under an effective magnetic field. We investigate how the applied magnetic field affects the Mott transition within mean-field theory and find that the critical hopping strength (t/U){sub c} increases with the applied field. The increase in the critical hopping follows the bandwidth of the Hofstadter butterfly at the given value of the magnetic field. We also calculate the magnetization and superfluid density within mean-field theory.
Scattering matrix theory for stochastic scalar fields.
Korotkova, Olga; Wolf, Emil
2007-05-01
We consider scattering of stochastic scalar fields on deterministic as well as on random media, occupying a finite domain. The scattering is characterized by a generalized scattering matrix which transforms the angular correlation function of the incident field into the angular correlation function of the scattered field. Within the accuracy of the first Born approximation this matrix can be expressed in a simple manner in terms of the scattering potential of the scatterer. Apart from determining the angular distribution of the spectral intensity of the scattered field, the scattering matrix makes it possible also to determine the changes in the state of coherence of the field produced on scattering.
Renormalization group analysis of turbulence. I - Basic theory
NASA Astrophysics Data System (ADS)
Yakhot, Victor; Orszag, Steven A.
The dynamic renormalization group (RNG) method is developed for hydrodynamic turbulence. This procedure, which uses dynamic scaling and invariance together with iterated perturbation methods, permits the evaluation of transport coefficients and transport equations for the large-scale (slow) modes. The RNG theory, which does not include any experimentally adjustable parameters, gives the following numerical values for important constants of turbulent flows: Kolmogorov constant for the inertial-range spectrum = 1.617; turbulent Prandtl number for high-Reynolds-number heat transfer = 0.7179; Batchelor constant = 1.161; and skewness factor = 0.4878. A differential transport model, is derived which is particularly useful near walls.
Summary of the working group on FEL theory
Pellegrini, C.
1984-01-01
The working group on FEL theory dedicated most of its discussions to topics relevant to the high gain regime in a free electron laser. In addition the area of interest was mainly restricted to FELs for the production of XUV radiation (<1000 A). A list of the topics that were felt to be relevant is: (1) characterization of the FEL high gain regime; (2) the amplified spontaneous emission mode of operation (ASE); (3) superradiance in FELs; (4) diffraction effects for high gain FELs; (5) noise and start-up; (6) coherence properties of the radiation for the ASE and superradiant FELS. 9 references.
Integrable perturbations of conformal field theories and Yetter-Drinfeld modules
Bücher, David; Runkel, Ingo
2014-11-15
In this paper we relate a problem in representation theory — the study of Yetter-Drinfeld modules over certain braided Hopf algebras — to a problem in two-dimensional quantum field theory, namely, the identification of integrable perturbations of a conformal field theory. A prescription that parallels Lusztig's construction allows one to read off the quantum group governing the integrable symmetry. As an example, we illustrate how the quantum group for the loop algebra of sl(2) appears in the integrable structure of the perturbed uncompactified and compactified free boson.
Comparisons and connections between mean field dynamo theory and accretion disc theory
NASA Astrophysics Data System (ADS)
Blackman, E. G.
2010-01-01
The origin of large scale magnetic fields in astrophysical rotators, and the conversion of gravitational energy into radiation near stars and compact objects via accretion have been subjects of active research for a half century. Magnetohydrodynamic turbulence makes both problems highly nonlinear, so both subjects have benefitted from numerical simulations.However, understanding the key principles and practical modeling of observations warrants testable semi-analytic mean field theories that distill the essential physics. Mean field dynamo (MFD) theory and alpha-viscosity accretion disc theory exemplify this pursuit. That the latter is a mean field theory is not always made explicit but the combination of turbulence and global symmetry imply such. The more commonly explicit presentation of assumptions in 20th century textbook MFDT has exposed it to arguably more widespread criticism than incurred by 20th century alpha-accretion theory despite complementary weaknesses. In the 21st century however, MFDT has experienced a breakthrough with a dynamical saturation theory that consistently agrees with simulations. Such has not yet occurred in accretion disc theory, though progress is emerging. Ironically however, for accretion engines, MFDT and accretion theory are presently two artificially uncoupled pieces of what should be a single coupled theory. Large scale fields and accretion flows are dynamically intertwined because large scale fields likely play a key role in angular momentum transport. I discuss and synthesize aspects of recent progress in MFDT and accretion disc theory to suggest why the two likely conspire in a unified theory.
Quantum field theory of the Casimir effect for real media
Mostepanenko, V.M.; Trunov, N.N.
1985-11-01
The quantum field theory is developed for the corrections to the Casimir force arising when the field penetrates the material of the plates. A new type of divergence arising from the corresponding modification of the boundary conditions is analyzed. General expressions are obtained for the vacuum energy of the electromagnetic field in the space between nonideal plates, and the actual corrections to the Casimir force are calculated in first-order perturbation theory in the penetration depth.
Universal behavior after a quantum quench in interacting field theories
NASA Astrophysics Data System (ADS)
Mitra, Aditi
The dynamics of an isolated quantum system represented by a field theory with O(N) symmetry, and in d>2 spatial dimensions, is investigated after a quantum quench from a disordered initial state to the critical point. A perturbative renormalization-group approach involving an expansion around d=4 is employed to study the time-evolution, and is supplemented by an exact solution of the Hartree-Fock equations in the large-N limit. The results show that the dynamics is characterized by a prethermal regime controlled by elastic dephasing where excitations propagate ballistically, and a light cone emerges in correlation functions in real space. The memory of the initial state, together with the absence of time-scales at the critical point, gives rise to universal power-law aging which is characterized by a new non-equilibrium short-time exponent. The dynamics of the entanglement following a quench is also explored, and reveals that while the time evolution of the entanglement entropy itself is not much different between a free bosonic theory and an interacting bosonic theory, the low-energy entanglement spectrum on the other hand shows clear signature of the non-equilibrium short-time exponent related to aging. This work was done in collaboration with Y. Lemonik (NYU), M. Tavora (NYU), A. Chiocchetta (SISSA), A. Maraga (SISSA), and A. Gambassi (SISSA). Supported by NSF-DMR 1303177.
Review and application of group theory to molecular systems biology
2011-01-01
In this paper we provide a review of selected mathematical ideas that can help us better understand the boundary between living and non-living systems. We focus on group theory and abstract algebra applied to molecular systems biology. Throughout this paper we briefly describe possible open problems. In connection with the genetic code we propose that it may be possible to use perturbation theory to explore the adjacent possibilities in the 64-dimensional space-time manifold of the evolving genome. With regards to algebraic graph theory, there are several minor open problems we discuss. In relation to network dynamics and groupoid formalism we suggest that the network graph might not be the main focus for understanding the phenotype but rather the phase space of the network dynamics. We show a simple case of a C6 network and its phase space network. We envision that the molecular network of a cell is actually a complex network of hypercycles and feedback circuits that could be better represented in a higher-dimensional space. We conjecture that targeting nodes in the molecular network that have key roles in the phase space, as revealed by analysis of the automorphism decomposition, might be a better way to drug discovery and treatment of cancer. PMID:21696623
Critical asymmetry in renormalization group theory for fluids.
Zhao, Wei; Wu, Liang; Wang, Long; Li, Liyan; Cai, Jun
2013-06-21
The renormalization-group (RG) approaches for fluids are employed to investigate critical asymmetry of vapour-liquid equilibrium (VLE) of fluids. Three different approaches based on RG theory for fluids are reviewed and compared. RG approaches are applied to various fluid systems: hard-core square-well fluids of variable ranges, hard-core Yukawa fluids, and square-well dimer fluids and modelling VLE of n-alkane molecules. Phase diagrams of simple model fluids and alkanes described by RG approaches are analyzed to assess the capability of describing the VLE critical asymmetry which is suggested in complete scaling theory. Results of thermodynamic properties obtained by RG theory for fluids agree with the simulation and experimental data. Coexistence diameters, which are smaller than the critical densities, are found in the RG descriptions of critical asymmetries of several fluids. Our calculation and analysis show that the approach coupling local free energy with White's RG iteration which aims to incorporate density fluctuations into free energy is not adequate for VLE critical asymmetry due to the inadequate order parameter and the local free energy functional used in the partition function.
On the stability of the asymptotically free scalar field theories
Shalaby, A M.
2015-03-30
Asymptotic freedom plays a vital role in our understanding of the theory of particle interactions. To have this property, one has to resort to a Non-abelian gauge theory with the number of colors equal to or greater than three (QCD). However, recent studies have shown that simple scalar field theories can possess this interesting property. These theories have non-Hermitian effective field forms but their classical potentials are bounded from above. In this work, we shall address the stability of the vacua of the bounded from above (−Φ{sup 4+n}) scalar field theories. Moreover, we shall cover the effect of the distribution of the Stokes wedges in the complex Φ-plane on the features of the vacuum condensate within these theories.
Splitting fields and general differential Galois theory
Trushin, Dmitry V
2010-11-11
An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on the search for prime differential ideals of special form in tensor products of differential rings. The main results demonstrating the work of the technique obtained are the theorem on the constructedness of the differential closure and the general theorem on the Galois correspondence for normal extensions. Bibliography: 14 titles.
Quantum revivals in conformal field theories in higher dimensions
NASA Astrophysics Data System (ADS)
Cardy, John
2016-10-01
We investigate the behavior of the return amplitude { F }(t)=| < {{\\Psi }}(0)| {{\\Psi }}(t)> | following a quantum quench in a conformal field theory (CFT) on a compact spatial manifold of dimension d-1 and linear size O(L), from a state | {{\\Psi }}(0)> of extensive energy with short-range correlations. After an initial gaussian decay { F }(t) reaches a plateau value related to the density of available states at the initial energy. However for d=3,4 this value is attained from below after a single oscillation. For a holographic CFT the plateau persists up to times at least O({σ }1/(d-1)L), where σ \\gg 1 is the dimensionless Stefan-Boltzmann constant. On the other hand for a free field theory on manifolds with high symmetry there are typically revivals at times t˜ {{integer}}× L. In particular, on a sphere {S}d-1 of circumference 2π L, there is an action of the modular group on { F }(t) implying structure near all rational values of t/L, similar to what happens for rational CFTs in d=2.
Larger Units: Theater Army, Army Group, Field Army
1984-09-01
LARGER UNITS: Theater Army, Army Group , Field Army St Fort LeawiivfoW, Kansas /A ’j>’" /\\(7 ’"VX <\\,» •«:-•$-(••’•.•->’-:-j Report...TYPE 3. DATES COVERED 00-00-1984 to 00-00-1984 4. TITLE AND SUBTITLE Larger Units: Theater Army, Army Group , Field Army 5a. CONTRACT NUMBER 5b...Bibliography No. 4 LARGER UNITS: THEATER ARMY—ARMY GROUP —FIELD ARMY by LTC Gary L. Bounds Combat Studies Institute U.S. Army Command and General Staff
Quiver theories for moduli spaces of classical group nilpotent orbits
NASA Astrophysics Data System (ADS)
Hanany, Amihay; Kalveks, Rudolph
2016-06-01
We approach the topic of Classical group nilpotent orbits from the perspective of the moduli spaces of quivers, described in terms of Hilbert series and generating functions. We review the established Higgs and Coulomb branch quiver theory constructions for A series nilpotent orbits. We present systematic constructions for BCD series nilpotent orbits on the Higgs branches of quiver theories defined by canonical partitions; this paper collects earlier work into a systematic framework, filling in gaps and providing a complete treatment. We find new Coulomb branch constructions for above minimal nilpotent orbits, including some based upon twisted affine Dynkin diagrams. We also discuss aspects of 3 d mirror symmetry between these Higgs and Coulomb branch constructions and explore dualities and other relationships, such as HyperKähler quotients, between quivers. We analyse all Classical group nilpotent orbit moduli spaces up to rank 4 by giving their unrefined Hilbert series and the Highest Weight Generating functions for their decompositions into characters of irreducible representations and/or Hall Littlewood polynomials.
Semiclassical theory of unimolecular dissociation induced by a laser field
NASA Technical Reports Server (NTRS)
Yuan, J.-M.; George, T. F.
1978-01-01
A semiclassical nonperturbative theory of direct photodissociation in a laser field is developed in which photon absorption and dissociation are treated in a unified fashion. This is achieved by visualizing nuclear dynamics as a representative particle moving on electronic-field surfaces. Methods are described for calculating dissociation rates and probabilities by Monte Carlo selection of initial conditions and integration of classical trajectories on these surfaces. This unified theory reduces to the golden rule expression in the weak-field and short-time limits, and predicts nonlinear behavior, i.e., breakdown of the golden rule expression in intense fields. Field strengths above which lowest-order perturbation theory fails to work have been estimated for some systems. Useful physical insights provided by the electronic-field representation have been illustrated. Intense field effects are discussed which are amenable to experimental observation. The semiclassical methods used here are also applicable to multiple-surface dynamics in fieldfree unimolecular and bimolecular reactions.
The tensor hierarchy of 8-dimensional field theories
NASA Astrophysics Data System (ADS)
Andino, Óscar Lasso; Ortín, Tomás
2016-10-01
We construct the tensor hierarchy of generic, bosonic, 8-dimensional field theories. We first study the form of the most general 8-dimensional bosonic theory with Abelian gauge symmetries only and no massive deformations. This study determines the tensors that occur in the Chern-Simons terms of the (electric and magnetic) field strengths and the action for the electric fields, which we determine. Having constructed the most general Abelian theory we study the most general gaugings of its global symmetries and the possible massive deformations using the embedding tensor formalism, constructing the complete tensor hierarchy using the Bianchi identities. We find the explicit form of all the field strengths of the gauged theory up to the 6-forms. Finally, we find the equations of motion comparing the Noether identities with the identities satisfied by the Bianchi identities themselves. We find that some equations of motion are not simply the Bianchi identities of the dual fields, but combinations of them.
Unambiguous formalism for higher order Lagrangian field theories
NASA Astrophysics Data System (ADS)
Campos, Cédric M.; de León, Manuel; Martín de Diego, David; Vankerschaver, Joris
2009-11-01
The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, and implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher order field theories. Several examples illustrate our construction.
Avoiding Haag's Theorem with Parameterized Quantum Field Theory
NASA Astrophysics Data System (ADS)
Seidewitz, Ed
2017-03-01
Under the normal assumptions of quantum field theory, Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that Haag's Theorem can be avoided when quantum field theory is formulated using an invariant, fifth path parameter in addition to the usual four position parameters, such that the Dyson perturbation expansion for the scattering matrix can still be reproduced. As a result, the parameterized formalism provides a consistent foundation for the interpretation of quantum field theory as used in practice and, perhaps, for better dealing with other mathematical issues.
Quantum Simulation of Quantum Field Theories in Trapped Ions
Casanova, J.; Lamata, L.; Egusquiza, I. L.; Gerritsma, R.; Roos, C. F.; Garcia-Ripoll, J. J.; Solano, E.
2011-12-23
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Quantum simulation of quantum field theories in trapped ions.
Casanova, J; Lamata, L; Egusquiza, I L; Gerritsma, R; Roos, C F; García-Ripoll, J J; Solano, E
2011-12-23
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Incorporation of generalized uncertainty principle into Lifshitz field theories
NASA Astrophysics Data System (ADS)
Faizal, Mir; Majumder, Barun
2015-06-01
In this paper, we will incorporate the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bosonic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into a non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle.
Incorporation of generalized uncertainty principle into Lifshitz field theories
Faizal, Mir; Majumder, Barun
2015-06-15
In this paper, we will incorporate the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bosonic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into a non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle.
Quantum Yang-Mills field theory
NASA Astrophysics Data System (ADS)
Frasca, Marco
2017-01-01
We show that the Dyson-Schwinger set of equations for the Yang-Mills theory can be exactly solved till the two-point function. This is obtained given a set of nonlinear waves solving the classical equations of motion. Translation invariance is maintained by the proper choice of the solution of the equation for the two-point function as devised by Coleman. The computation of the Dyson-Schwinger equations is performed in the same way as devised by Bender, Milton and Savage providing a set of partial differential equations whose proof of existence of the solutions is standard. So, the correlation functions of the theory could be proved to exist and the two-point function manifests a mass gap.
Killing vector fields and harmonic superfield theories
Groeger, Josua
2014-09-15
The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, also referred to as harmonic, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of this harmonic action and prove three different Noether theorems in this context. En passant, we provide a homogeneous treatment of five characterisations of Killing vector fields on semi-Riemannian supermanifolds, thus filling a gap in the literature.
Killing vector fields and harmonic superfield theories
NASA Astrophysics Data System (ADS)
Groeger, Josua
2014-09-01
The harmonic action functional allows a natural generalisation to semi-Riemannian supergeometry, also referred to as harmonic, which resembles the supersymmetric sigma models studied in high energy physics. We show that Killing vector fields are infinitesimal supersymmetries of this harmonic action and prove three different Noether theorems in this context. En passant, we provide a homogeneous treatment of five characterisations of Killing vector fields on semi-Riemannian supermanifolds, thus filling a gap in the literature.
Circular Wilson loops in defect conformal field theory
NASA Astrophysics Data System (ADS)
Aguilera-Damia, Jeremías; Correa, Diego H.; Giraldo-Rivera, Victor I.
2017-03-01
We study a D3-D5 system dual to a conformal field theory with a codimension-one defect that separates regions where the ranks of the gauge groups differ by k. With the help of this additional parameter, as observed by Nagasaki, Tanida and Yamaguchi, one can define a double scaling limit in which the quantum corrections are organized in powers of λ/k 2, which should allow to extrapolate results between weak and strong coupling regimes. In particular we consider a radius R circular Wilson loop placed at a distance L, whose internal space orientation is given by an angle χ. We compute its vacuum expectation value and show that, in the double scaling limit and for small χ and small L/R, weak coupling results can be extrapolated to the strong coupling limit.
Hydrodynamic transport functions from quantum kinetic field theory
NASA Astrophysics Data System (ADS)
Calzetta, E. A.; Hu, B. L.; Ramsey, S. A.
2000-06-01
Starting from the quantum kinetic field theory [E. Calzetta and B. L. Hu, Phys. Rev. D 37, 2878 (1988)] constructed from the closed-time-path (CTP), two-particle-irreducible (2PI) effective action we show how to compute from first principles the shear and bulk viscosity functions in the hydrodynamic-thermodynamic regime. For a real scalar field with λΦ4 self-interaction we need to include four-loop graphs in the equation of motion. This work provides a microscopic field-theoretical basis to the ``effective kinetic theory'' proposed by Jeon and Yaffe [S. Jeon and L. G. Yaffe, Phys. Rev. D 53, 5799 (1996)], while our result for the bulk viscosity reproduces their expression derived from linear-response theory and the imaginary-time formalism of thermal field theory. Though unavoidably involved in calculations of this sort, we feel that the approach using fundamental quantum kinetic field theory is conceptually clearer and methodically simpler than the effective kinetic theory approach, as the success of the latter requires a clever rendition of diagrammatic resummations which is neither straightforward nor fail-safe. Moreover, the method based on the CTP-2PI effective action illustrated here for a scalar field can be formulated entirely in terms of functional integral quantization, which makes it an appealing method for a first-principles calculation of transport functions of a thermal non-Abelian gauge theory, e.g., QCD quark-gluon plasma produced from heavy ion collisions.
On the theory of group generation of stars
NASA Technical Reports Server (NTRS)
Zhilyayev, B. Y.; Porfiryev, V. V.; Shulman, L. M.
1973-01-01
The hypothesis proposed is that topology of a rotating gaseous cloud can be variable in the contraction process. Due to rotation an originally spherical cloud is transformed into a toroidal body. The contraction of a thin torus is considered with different suppositions on cooling the gas. In the determined time the torus will become gravitationally unstable. The excitation of Jeans' waves is shown to result in the disintegration of the torus into fragments. The number of the fragments and their mass distributions are calculated. The proposed hypothesis on toroidal stages in stellar evolution can remove some difficulties in the theory of structure and evolution of stars, such as absence of limitary stars, distribution of rotation velocities of early-type stars, origin of poloidal magnetic fields and decline rotators with the magnetic axis orthogonal to the axis of rotation.
Geometrical Effective Action: Gauge Field Theory Without Ghosts.
NASA Astrophysics Data System (ADS)
Paris, Carmen Molina
Ghosts were invented by Feynman (1) in 1962 while trying to construct a quantum theory of gravity. Having convinced himself that there was no way in which the gravitational field could consistently escape quantization in a universe where everything else is subject to the laws of quantum mechanics, he was trying to see how these laws would work when applied to spacetime curvature. The first obstacle he faced was the non-Abelian character of the diffeomorphism group (the gauge group of gravity) which forces the gravitational field to act partly as its own source. In the language of Feynman graphs this means that gravitational charge (stress-energy) is carried by graviton lines as well as by all other lines and hence leaks all over every graph. Feynman's key idea for solving the problem was to replace every Feynman propagator by its equivalent, an advanced Green's function minus a positive-frequency Wightman function, and to throw away all noncausal loops of advanced Green's functions^1, obtaining thereby a mode sum over tree functions. It is easy to show that tree functions are gauge invariant provided the external lines bear only physical mode functions. Feynman therefore proposed to restrict the mode sums to physical modes, a procedure that not only secures gauge invariance but unitarity as well. But there is a difficulty: Because the physical mode functions are defined in a special frame, the procedure is not manifestly Lorentz invariant ^2. Feynman was able to show that deletion of the nonphysical modes is equivalent to subtracting, from the contribution of every closed loop, that of another (Lorentz invariant) loop propagating a particle having spin 1 (or one less than that of the gauge field). This is the ghost. Because its contribution is subtracted, it is a fermion. Feynman's discovery, and the work that it stimulated, made it seem as if the quantum theory of gauge fields cannot even be formulated without ghosts. It is the purpose of this dissertation to show
Lattice Study of Magnetic Catalysis in Graphene Effective Field Theory
NASA Astrophysics Data System (ADS)
Winterowd, Christopher; Detar, Carleton; Zafeiropoulos, Savvas
2016-03-01
The discovery of graphene ranks as one of the most important developments in condensed matter physics in recent years. As a strongly interacting system whose low-energy excitations are described by the Dirac equation, graphene has many similarities with other strongly interacting field theories, particularly quantum chromodynamics (QCD). Graphene, along with other relativistic field theories, have been predicted to exhibit spontaneous symmetry breaking (SSB) when an external magnetic field is present. Using nonperturbative methods developed to study QCD, we study the low-energy effective field theory (EFT) of graphene subject to an external magnetic field. We find strong evidence supporting the existence of SSB at zero-temperature and characterize the dependence of the chiral condensate on the external magnetic field. We also present results for the mass of the Nambu-Goldstone boson and the dynamically generated quasiparticle mass that result from the SSB.
Screening of scalar fields in Dirac-Born-Infeld theory
NASA Astrophysics Data System (ADS)
Burrage, Clare; Khoury, Justin
2014-07-01
We study a new screening mechanism which is present in Dirac-Born-Infeld (DBI)-like theories. A scalar field with a DBI-like Lagrangian is minimally coupled to matter. In the vicinity of sufficiently dense sources, nonlinearities in the scalar dominate and result in an approximately constant acceleration on a test particle, thereby suppressing the scalar force relative to gravity. Unlike generic P(X) or chameleon theories, screening happens within the regime of validity of the effective field theory thanks to the DBI symmetry. We derive an exact form for the field profile around multiple sources and determine the constraints on the theory parameters from tests of gravity. Perturbations around the spherically-symmetric background propagate superluminally, but we argue for a chronology protection analogous to Galileons. This is the first example of a screening mechanism for which quantum corrections to the theory are under control and exact solutions to cosmological N-body problems can be found.
Topological Field Theory of Time-Reversal Invariant Insulators
Qi, Xiao-Liang; Hughes, Taylor; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
We show that the fundamental time reversal invariant (TRI) insulator exists in 4 + 1 dimensions, where the effective field theory is described by the 4 + 1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2 + 1 dimensions. The TRI quantum spin Hall insulator in 2 + 1 dimensions and the topological insulator in 3 + 1 dimension can be obtained as descendants from the fundamental TRI insulator in 4 + 1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the Z{sub 2} topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant {alpha} = e{sup 2}/hc. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.
Conceptual Developments of 20th Century Field Theories
NASA Astrophysics Data System (ADS)
Cao, Tian Yu
1998-06-01
This volume provides a broad synthesis of conceptual developments of twentieth century field theories, from the general theory of relativity to quantum field theory and gauge theory. The book traces the foundations and evolution of these theories within a historio-critical context. Theoretical physicists and students of theoretical physics will find this a valuable account of the foundational problems of their discipline that will help them understand the internal logic and dynamics of theoretical physics. It will also provide professional historians and philosophers of science, particularly philosophers of physics, with a conceptual basis for further historical, cultural and sociological analysis of the theories discussed. Finally, the scientifically qualified general reader will find in this book a deeper analysis of contemporary conceptions of the physical world than can be found in popular accounts of the subject.
Conceptual Developments of 20th Century Field Theories
NASA Astrophysics Data System (ADS)
Cao, Tian Yu
1997-02-01
This volume provides a broad synthesis of conceptual developments of twentieth century field theories, from the general theory of relativity to quantum field theory and gauge theory. The book traces the foundations and evolution of these theories within a historio-critical context. Theoretical physicists and students of theoretical physics will find this a valuable account of the foundational problems of their discipline that will help them understand the internal logic and dynamics of theoretical physics. It will also provide professional historians and philosophers of science, particularly philosophers of physics, with a conceptual basis for further historical, cultural and sociological analysis of the theories discussed. Finally, the scientifically qualified general reader will find in this book a deeper analysis of contemporary conceptions of the physical world than can be found in popular accounts of the subject.
Using Self Consistent Field Theory on Polymeric Mixtures
NASA Astrophysics Data System (ADS)
von Konigslow, Kier; Park, Chul; Thompson, Russell
The ability to predict the solubility of a particular solvent in a polymer fluid is essential to the production of polymer foams. For the past 40 years, the primary model employed to this end has been an expansion of Flory-Huggins lattice fluid theory developed by Sanchez and Lacombe (S-L theory). S-L theory, while useful in the uniform limit, is limited to homogeneous systems. Self-Consistent Field Theory (SCFT), which has long been in use in polymer physics, is a mean-field theory capable of modeling the equilibrium behaviour of both homogeneous and inhomogeneous systems. We are investigating whether SCFT, applied to polymer-solvent mixtures, is in agreement with SL-theory in the homogeneous limit. Should this prove successful, we hope to use SCFT to model more general mixtures, including inhomogeneous nanocellular polymer foam systems.
The Theory of Quantized Fields. III
DOE R&D Accomplishments Database
Schwinger, J.
1953-05-01
In this paper we discuss the electromagnetic field, as perturbed by a prescribed current. All quantities of physical interest in various situations, eigenvalues, eigenfunctions, and transformation probabilities, are derived from a general transformation function which is expressed in a non-Hermitian representation. The problems treated are: the determination of the energy-momentum eigenvalues and eigenfunctions for the isolated electromagnetic field, and the energy eigenvalues and eigenfunctions for the field perturbed by a time-independent current that departs from zero only within a finite time interval, and for a time-dependent current that assumes non-vanishing time-independent values initially and finally. The results are applied in a discussion of the intra-red catastrophe and of the adiabatic theorem. It is shown how the latter can be exploited to give a uniform formulation for all problems requiring the evaluation of transition probabilities or eigenvalue displacements.
System theory on group manifolds and coset spaces.
NASA Technical Reports Server (NTRS)
Brockett, R. W.
1972-01-01
The purpose of this paper is to study questions regarding controllability, observability, and realization theory for a particular class of systems for which the state space is a differentiable manifold which is simultaneously a group or, more generally, a coset space. We show that it is possible to give rather explicit expressions for the reachable set and the set of indistinguishable states in the case of autonomous systems. We also establish a type of state space isomorphism theorem. Our objective is to reduce all questions about the system to questions about Lie algebras generated from the coefficient matrices entering in the description of the system and in that way arrive at conditions which are easily visualized and tested.
Torque anomaly in quantum field theory
NASA Astrophysics Data System (ADS)
Fulling, S. A.; Mera, F. D.; Trendafilova, C. S.
2013-02-01
The expectation values of energy density and pressure of a quantum field inside a wedge-shaped region appear to violate the expected relationship between torque and total energy as a function of angle. In particular, this is true of the well-known Deutsch-Candelas stress tensor for the electromagnetic field, whose definition requires no regularization except possibly at the vertex. Unlike a similar anomaly in the pressure exerted by a reflecting boundary against a perpendicular wall, this problem cannot be dismissed as an artifact of an ad hoc regularization.
Theory of back-surface-field solar cells
NASA Technical Reports Server (NTRS)
Vonroos, O.
1979-01-01
Report describes simple concise theory of back-surface-field (BSF) solar cells (npp + junctions) based on Shockley's depletion-layer approximation and cites superiority of two-junction devices over conventional unijunction cells.
Exotic dual of type II double field theory
NASA Astrophysics Data System (ADS)
Bergshoeff, Eric A.; Hohm, Olaf; Riccioni, Fabio
2017-04-01
We perform an exotic dualization of the Ramond-Ramond fields in type II double field theory, in which they are encoded in a Majorana-Weyl spinor of O (D , D). Starting from a first-order master action, the dual theory in terms of a tensor-spinor of O (D , D) is determined. This tensor-spinor is subject to an exotic version of the (self-)duality constraint needed for a democratic formulation. We show that in components, reducing O (D , D) to GL (D), one obtains the expected exotically dual theory in terms of mixed Young tableaux fields. To this end, we generalize exotic dualizations to self-dual fields, such as the 4-form in type IIB string theory.
Constrained field theories on spherically symmetric spacetimes with horizons
NASA Astrophysics Data System (ADS)
Fernandes, Karan; Lahiri, Amitabha; Ghosh, Suman
2017-02-01
We apply the Dirac-Bergmann algorithm for the analysis of constraints to gauge theories defined on spherically symmetric black hole backgrounds. We find that the constraints for a given theory are modified on such spacetimes through the presence of additional contributions from the horizon. As a concrete example, we consider the Maxwell field on a black hole background, and determine the role of the horizon contributions on the dynamics of the theory.
Experimentally verifiable Yang-Mills spin 2 gauge theory of gravity with group U(1) x SU(2)
NASA Astrophysics Data System (ADS)
Peng, Huei
1988-06-01
A Yang-Mills spin 2 gauge theory of gravity is proposed. Based on both the verification of the helicity 2 property of the SU(2) gauge bosons of the theory and the agreement of the theory with most observational and experimental evidence, it is argued that the theory is truly a gravitational theory. Generation by the 4-momentum P sup mu of a fermion of U(1) x SU(2) internal symmetry group for gravity, but not the transformation group T sup 4 is demonstrated. It is shown that the U(1) x SU(2) group represents the time displacement and rotation in ordinary space. Thereby internal space associated with gravity is identical with Minkowski spacetime, so a gauge potential of gravity carries two spacetime indices. Then it is verified that the SU(2) gravitational boson has helicity 2. This theory predicts experimentally verifiable gravitomagnetic fields 4 times smaller than that of general relativity.
Field theories and exact stochastic equations for interacting particle systems
Andreanov, Alexei; Lefevre, Alexandre; Biroli, Giulio; Bouchaud, Jean-Philippe
2006-09-15
We consider the dynamics of interacting particles with reaction and diffusion. Starting from the underlying discrete stochastic jump process we derive a general field theory describing the dynamics of the density field, which we relate to an exact stochastic equation on the density field. We show how our field theory maps onto the original Doi-Peliti formalism, allowing us to clarify further the issue of the 'imaginary' Langevin noise that appears in the context of reaction-diffusion processes. Our procedure applies to a wide class of problems and is related to large deviation functional techniques developed recently to describe fluctuations of nonequilibrium systems in the hydrodynamic limit.
Perturbation Theory of Massive Yang-Mills Fields
DOE R&D Accomplishments Database
Veltman, M.
1968-08-01
Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.
Constrained variational calculus for higher order classical field theories
NASA Astrophysics Data System (ADS)
Campos, Cédric M.; de León, Manuel; Martín de Diego, David
2010-11-01
We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.
A Guided Inquiry Activity for Teaching Ligand Field Theory
ERIC Educational Resources Information Center
Johnson, Brian J.; Graham, Kate J.
2015-01-01
This paper will describe a guided inquiry activity for teaching ligand field theory. Previous research suggests the guided inquiry approach is highly effective for student learning. This activity familiarizes students with the key concepts of molecular orbital theory applied to coordination complexes. Students will learn to identify factors that…
Near-field environment/processes working group summary
Murphy, W.M.
1995-09-01
This article is a summary of the proceedings of a group discussion which took place at the Workshop on the Role of Natural Analogs in Geologic Disposal of High-Level Nuclear Waste in San Antonio, Texas on July 22-25, 1991. The working group concentrated on the subject of the near-field environment to geologic repositories for high-level nuclear waste. The near-field environment may be affected by thermal perturbations from the waste, and by disturbances caused by the introduction of exotic materials during construction of the repository. This group also discussed the application of modelling of performance-related processes.
Holographic thermal field theory on curved spacetimes
NASA Astrophysics Data System (ADS)
Marolf, Donald; Rangamani, Mukund; Wiseman, Toby
2014-03-01
The AdS/CFT correspondence relates certain strongly-coupled CFTs with large effective central charge ceff to semi-classical gravitational theories with AdS asymptotics. We describe recent progress in understanding gravity duals for CFTs on non-trivial spacetimes at finite temperature, both in and out of equilibrium. Such gravity methods provide powerful new tools to access the physics of these strongly-coupled theories, which often differs qualitatively from that found at weak coupling. Our discussion begins with basic aspects of AdS/CFT and progresses through thermal CFTs on the Einstein Static Universe and on periodically identified Minkowski spacetime. In the latter context we focus on states describing so-called plasma-balls, which become stable at large ceff. We then proceed to out-of-equilibrium situations associated with dynamical bulk black holes. In particular, the non-compact nature of these bulk black holes allows stationary solutions with non-Killing horizons that describe time-independent flows of CFT plasma. As final a topic we consider CFTs on black hole spacetimes. This discussion provides insight into how the CFT transports heat between general heat sources and sinks of finite size. In certain phases the coupling to small sources can be strongly suppressed, resulting in negligible heat transport despite the presence of a deconfined plasma with sizeable thermal conductivity. We also present a new result, explaining how this so-called droplet behaviour is related to confinement via a change of conformal frame.
The Lagrangian-Hamiltonian formalism for higher order field theories
NASA Astrophysics Data System (ADS)
Vitagliano, Luca
2010-06-01
We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.
Non-perturbative methods in relativistic field theory
Franz Gross
2013-03-01
This talk reviews relativistic methods used to compute bound and low energy scattering states in field theory, with emphasis on approaches that John Tjon and I discussed (and argued about) together. I compare the Bethe–Salpeter and Covariant Spectator equations, show some applications, and then report on some of the things we have learned from the beautiful Feynman–Schwinger technique for calculating the exact sum of all ladder and crossed ladder diagrams in field theory.
Renormalized parameters and perturbation theory in dynamical mean-field theory for the Hubbard model
NASA Astrophysics Data System (ADS)
Hewson, A. C.
2016-11-01
We calculate the renormalized parameters for the quasiparticles and their interactions for the Hubbard model in the paramagnetic phase as deduced from the low-energy Fermi-liquid fixed point using the results of a numerical renormalization-group calculation (NRG) and dynamical mean-field theory (DMFT). Even in the low-density limit there is significant renormalization of the local quasiparticle interaction U ˜, in agreement with estimates based on the two-particle scattering theory of J. Kanamori [Prog. Theor. Phys. 30, 275 (1963), 10.1143/PTP.30.275]. On the approach to the Mott transition we find a finite ratio for U ˜/D ˜ , where 2 D ˜ is the renormalized bandwidth, which is independent of whether the transition is approached by increasing the on-site interaction U or on increasing the density to half filling. The leading ω2 term in the self-energy and the local dynamical spin and charge susceptibilities are calculated within the renormalized perturbation theory (RPT) and compared with the results calculated directly from the NRG-DMFT. We also suggest, more generally from the DMFT, how an approximate expression for the q ,ω spin susceptibility χ (q ,ω ) can be derived from repeated quasiparticle scattering with a local renormalized scattering vertex.
X(3872) in Effective Field Theory
Fleming, S.; Mehen, T.
2009-12-17
If the X(3872) resonance is a shallow boundstate of a the charm mesons D{sup 0}D-bar*{sup 0} and D*{sup 0}D-bar{sup 0}, it can be described by an effective theory of nonrelativistic D mesons coupled to nonrelativistic pions (X-EFT). In this talk, I give a brief overview of the X(3872), followed by a short review of X-EFT. I end my talk with results from calculations of the the next-to-leading-order correction to the partial decay width {gamma}[X{yields}D{sup 0}D-bar{sup 0}{pi}{sup 0}], and the decay of X(3872) to P-wave quarkonia.
Radiation reaction in quantum field theory
NASA Astrophysics Data System (ADS)
Higuchi, Atsushi
2002-11-01
We investigate radiation-reaction effects for a charged scalar particle accelerated by an external potential realized as a space-dependent mass term in quantum electrodynamics. In particular, we calculate the position shift of the final-state wave packet of the charged particle due to radiation at lowest order in the fine structure constant α and in the small ħ approximation. We show that it disagrees with the result obtained using the Lorentz-Dirac formula for the radiation-reaction force, and that it agrees with the classical theory if one assumes that the particle loses its energy to radiation at each moment of time according to the Larmor formula in the static frame of the potential. However, the discrepancy is much smaller than the Compton wavelength of the particle. We also point out that the electromagnetic correction to the potential has no classical limit.
Democracy of internal symmetries in supersymmetrical quantum field theory
Lopuszanski, J.T.
1981-12-01
The freedom of choice of some discrete and internal symmetries in the supersymmetric, massive, interacting quantum field theory is discussed. It is shown that the discrete symmetry consisting of changing the sign of some (not all) scalar fields is incompatible with the supersymmetric structure of the theory. It is further demonstrated that an internal symmetry which transforms only some of the fields of fixed spin leaving the other fields invariant and which acts nontrivially on the supercharges can not be admitted as a symmetry; although it can be a good internal symmetry in absence of supersymmetric covariance. Moreover, in case of a model consisting of scalar, spinor and vector fields even a symmetry which transforms all of the scalar (vector) fields leaving spinor and vector (scalar) fields unaffected is ruled out provided it acts nontrivially on some of the supercharges.
Statistical field theory description of inhomogeneous polarizable soft matter
NASA Astrophysics Data System (ADS)
Martin, Jonathan M.; Li, Wei; Delaney, Kris T.; Fredrickson, Glenn H.
2016-10-01
We present a new molecularly informed statistical field theory model of inhomogeneous polarizable soft matter. The model is based on fluid elements, referred to as beads, that can carry a net monopole of charge at their center of mass and a fixed or induced dipole through a Drude-type distributed charge approach. The beads are thus polarizable and naturally manifest attractive van der Waals interactions. Beyond electrostatic interactions, beads can be given soft repulsions to sustain fluid phases at arbitrary densities. Beads of different types can be mixed or linked into polymers with arbitrary chain models and sequences of charged and uncharged beads. By such an approach, it is possible to construct models suitable for describing a vast range of soft-matter systems including electrolyte and polyelectrolyte solutions, ionic liquids, polymerized ionic liquids, polymer blends, ionomers, and block copolymers, among others. These bead models can be constructed in virtually any ensemble and converted to complex-valued statistical field theories by Hubbard-Stratonovich transforms. One of the fields entering the resulting theories is a fluctuating electrostatic potential; other fields are necessary to decouple non-electrostatic interactions. We elucidate the structure of these field theories, their consistency with macroscopic electrostatic theory in the absence and presence of external electric fields, and the way in which they embed van der Waals interactions and non-uniform dielectric properties. Their suitability as a framework for computational studies of heterogeneous soft matter systems using field-theoretic simulation techniques is discussed.
Very special relativity as a background field theory
NASA Astrophysics Data System (ADS)
Ilderton, Anton
2016-08-01
We consider violation of Lorentz invariance in QED induced by a very high frequency background wave. An effective theory is obtained by averaging observables over the rapid field oscillations. This preserves Ward identities and restores translation invariance below the high-frequency scale, but only partial Lorentz invariance: we show that the effective theory is C-invariant SIM(2)-QED in very special relativity. Averaging leads to the nonlocal terms familiar from SIM(2) theories, while the short-distance behavior of the background field fermion propagator generates the infinite number of higher-order vertices of SIM(2)-QED.
Towards field theory in spaces with multivolume junctions
NASA Astrophysics Data System (ADS)
Fomin, P. I.; Shtanov, Yu V.
2002-06-01
We consider a spacetime formed by several pieces with common timelike boundary which plays the role of a junction between them. We establish junction conditions for fields of various spins and derive the resulting laws of wave propagation through the junction, which turn out to be quite similar for fields of all spins. As an application, we consider the case of multivolume junctions in four-dimensional spacetime that may arise in the context of the theory of quantum creation of a closed universe on the background of a big mother universe. The theory developed can also be applied to braneworld models and to the superstring theory.
Fundamental string solutions in open string field theories
Michishita, Yoji
2006-02-15
In Witten's open cubic bosonic string field theory and Berkovits' superstring field theory we investigate solutions of the equations of motion with appropriate source terms, which correspond to Callan-Maldacena solution in Born-Infeld theory representing fundamental strings ending on the D-branes. The solutions are given in order by order manner, and we show some full order properties in the sense of {alpha}{sup '} expansion. In superstring case we show that the solution is 1/2 BPS in full order.
Field theory on R×S 3 topology. V: SU 2 gauge theory
NASA Astrophysics Data System (ADS)
Carmeli, M.; Malin, S.
1987-02-01
A gauge theory on R×S 3 topology is developed. It is a generalization to the previously obtained field theory on R×S 3 topology and in which equations of motion were obtained for a scalar particle, a spin one-half particle, the electromagnetic field of magnetic moments, and a Shrödinger-type equation, as compared to ordinary field equations defined on a Minkowskian manifold. The new gauge field equations are presented and compared to the ordinary Yang-Mills field equations, and the mathematical and physical differences between them are discussed.
Protected gates for topological quantum field theories
NASA Astrophysics Data System (ADS)
Koenig, Robert
2015-03-01
We give restrictions on the locality-preserving unitary automorphisms U, which are protected gates, for topologically ordered systems. For arbitrary anyon models, we show that such unitaries only generate a finite group, and hence do not provide universality. For abelian anyon models, we find that the logical action of U is contained in a proper subgroup of the generalized Clifford group. In the case D(?2), which describes Kitaev's toric code, this represents a tightening of statement previously obtained within the stabilizer framework (PRL 110:170503). For non-abelian models, we find that such automorphisms are very limited: for example, there is no non-trivial gate for Fibonacci anyons. For Ising anyons, protected gates are elements of the Pauli group. These results are derived by relating such automorphisms to symmetries of the underlying anyon model: protected gates realize automorphisms of the Verlinde algebra. We additionally use the compatibility with basis changes to characterize the logical action. This is joint work with M. Beverland, F. Pastawski, J. Preskill and S. Sijher.
Ordinary versus PT-symmetric Φ³ quantum field theory
Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele
2012-04-02
A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric igΦ³ quantum field theory. This quantum field theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p²+ix³, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian gΦ³ quantum field theory with those of the PT-symmetric igΦ³ quantum field theory. It is shown that while the conventional gΦ³ theory in d=6 dimensions is asymptotically free, the igΦ³ theory is like a gΦ⁴ theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.
Group theory, entropy and the third law of thermodynamics
NASA Astrophysics Data System (ADS)
Canturk, Bilal; Oikonomou, Thomas; Bagci, G. Baris
2017-02-01
Curado et al. (2016) have recently studied the axiomatic structure and the universality of a three-parameter trace-form entropy inspired by the group-theoretical structure. In this work, we study the group-theoretical entropy S a , b , r in the context of the third law of thermodynamics where the parameters { a , b , r } are all independent. We show that this three-parameter entropy expression can simultaneously satisfy the third law of thermodynamics and the three Khinchin axioms, namely continuity, concavity and expansibility only when the parameter b is set to zero. In other words, it is thermodynamically valid only as a two-parameter generalization Sa,r. Moreover, the restriction set by the third law i.e., the condition b = 0, is important in the sense that the so obtained two-parameter group-theoretical entropy becomes extensive only when this condition is met. We also illustrate the interval of validity of the third law using the one-dimensional Ising model with no external field. Finally, we show that the Sa,r is in the same universality class as that of the Kaniadakis entropy for 0 < r < 1 while it has a distinct universality class in the interval - 1 < r < 0.
Effective Field Theories from Soft Limits of Scattering Amplitudes.
Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Trnka, Jaroslav
2015-06-05
We derive scalar effective field theories-Lagrangians, symmetries, and all-from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist.
On classification of extremal non-holomorphic conformal field theories
NASA Astrophysics Data System (ADS)
Tener, James E.; Wang, Zhenghan
2017-03-01
Rational chiral conformal field theories are organized according to their genus, which consists of a modular tensor category C and a central charge c. A long-term goal is to classify unitary rational conformal field theories based on a classification of unitary modular tensor categories. We conjecture that for any unitary modular tensor category C , there exists a unitary chiral conformal field theory V so that its modular tensor category {{C}V} is C . In this paper, we initiate a mathematical program in and around this conjecture. We define a class of extremal vertex operator algebras with minimal conformal dimensions as large as possible for their central charge, and non-trivial representation theory. We show that there are finitely many different characters of extremal vertex operator algebras V possessing at most three different irreducible modules. Moreover, we list all of the possible characters for such vertex operator algebras with c≤slant 48 .
Comments on conformal Killing vector fields and quantum field theory
Brown, M.R.; Ottewill, A.C.; Siklos, S.T.C.
1982-10-15
We give a comprehensive analysis of those vacuums for flat and conformally flat space-times which can be defined by timelike, hypersurface-orthogonal, conformal Killing vector fields. We obtain formulas for the difference in stress-energy density between any two such states and display the correspondence with the renormalized stress tensors. A brief discussion is given of the relevance of these results to quantum-mechanical measurements made by noninertial observers moving through flat space.
Graphene, Lattice Field Theory and Symmetries
Drissi, L. B.; Bousmina, M.; Saidi, E. H.
2011-02-15
Borrowing ideas from tight binding model, we propose a board class of lattice field models that are classified by non simply laced Lie algebras. In the case of A{sub N-1{approx_equal}}su(N) series, we show that the couplings between the quantum states living at the first nearest neighbor sites of the lattice L{sub suN} are governed by the complex fundamental representations N-bar and N of su(N) and the second nearest neighbor interactions are described by its adjoint N-bar x N. The lattice models associated with the leading su(2), su(3), and su(4) cases are explicitly studied and their fermionic field realizations are given. It is also shown that the su(2) and su(3) models describe the electronic properties of the acetylene chain and the graphene, respectively. It is established as well that the energy dispersion of the first nearest neighbor couplings is completely determined by the A{sub N} roots {alpha} through the typical dependence N/2+{Sigma}{sub roots} cos(k.{alpha} with k the wave vector.Other features such as the SO(2N) extension and other applications are also discussed.
DBI scalar field theory for QGP hydrodynamics
NASA Astrophysics Data System (ADS)
Nastase, Horatiu
2016-07-01
A way to describe the hydrodynamics of the quark-gluon plasma using a Dirac-Born-Infeld (DBI) action is proposed, based on the model found by Heisenberg for high energy scattering of nucleons. The expanding plasma is described as a shockwave in a DBI model for a real scalar standing in for the pion, and I show that one obtains a fluid description in terms of a relativistic fluid that near the shock is approximately ideal (η ≃0 ) and conformal. One can introduce an extra term inside the square root of the DBI action that generates a shear viscosity term in the energy-momentum tensor near the shock, as well as a bulk viscosity, and regulates the behavior of the energy density at the shock, making it finite. The resulting fluid satisfies the relativistic Navier-Stokes equation with uμ,ρ ,P ,η defined in terms of ϕ and its derivatives. One finds a relation between the parameters of the theory and the quark-gluon plasma thermodynamics, α /β2=η /(s T ), and by fixing α and β from usual (low multiplicity) particle scattering, one finds T ∝mπ.
Topics in lattice QCD and effective field theory
NASA Astrophysics Data System (ADS)
Buchoff, Michael I.
Quantum Chromodynamics (QCD) is the fundamental theory that governs hadronic physics. However, due to its non-perturbative nature at low-energy/long distances, QCD calculations are difficult. The only method for performing these calculations is through lattice QCD. These computationally intensive calculations approximate continuum physics with a discretized lattice in order to extract hadronic phenomena from first principles. However, as in any approximation, there are multiple systematic errors between lattice QCD calculation and actual hardronic phenomena. Developing analytic formulae describing the systematic errors due to the discrete lattice spacings is the main focus of this work. To account for these systematic effects in terms of hadronic interactions, effective field theory proves to be useful. Effective field theory (EFT) provides a formalism for categorizing low-energy effects of a high-energy fundamental theory as long as there is a significant separation in scales. An example of this is in chiral perturbation theory (chiPT), where the low-energy effects of QCD are contained in a mesonic theory whose applicability is a result of a pion mass smaller than the chiral breaking scale. In a similar way, lattice chiPT accounts for the low-energy effects of lattice QCD, where a small lattice spacing acts the same way as the quark mass. In this work, the basics of this process are outlined, and multiple original calculations are presented: effective field theory for anisotropic lattices, I=2 pipi scattering for isotropic, anisotropic, and twisted mass lattices. Additionally, a combination of effective field theory and an isospin chemical potential on the lattice is proposed to extract several computationally difficult scattering parameters. Lastly, recently proposed local, chiral lattice actions are analyzed in the framework of effective field theory, which illuminates various challenges in simulating such actions.
Spinor field theory at finite temperature in the early Universe
NASA Astrophysics Data System (ADS)
Banerjee, N.; Mallik, S.
1992-01-01
We consider the Dirac field on a spatially flat Robertson-Walker space-time. We find the exact expression for the Dirac propagator for an arbitrary scale factor in the real-time formulation of finite-temperature field theory. The mode functions used in the construction satisfy uncoupled ordinary differential equations.
Medical Argument and Field Theory: The Laetrile Case.
ERIC Educational Resources Information Center
Dunbar, Nancy R.
One approach to field theory in argumentation begins with a description of argumentation and, by identifying similarities or regularities in discursive practice, attempts to induce the nature and characteristics of a field. The controversy surrounding the use of Laetrile, a proposed cancer treatment, provides an example of this approach. Assuming…
Hermeneutical Field Theory and the Structural Character of Understanding.
NASA Astrophysics Data System (ADS)
Whitehouse, William Leonard
Through a series of exploratory case studies focusing on hermeneutics, phenomenology, relativity, field theory, quantum mechanics, chronobiology, chaos theory, holographic theory and various aspects of mathematics, a set of hermeneutical constraints and degrees of freedom are generated. There are a set of eight field equations given in the thesis which give qualitative symbolic expression to the aforementioned spectrum of constraints and degrees of freedom that constitute the structural character of understanding. However, as is sometimes the case with their quantitative mathematical counterparts, the hermeneutical field equations are capable of giving a variety of descriptions or solutions for one and the same set of conditions. The task, therefore, is to try to sort out those solutions which have reflective properties with respect to the structural character of reality from those which do not have such properties. The thesis addresses this task by introducing the idea of hermeneutical field theory. In this theory the notion of a semiotic operator or semiotic quantum plays a central role. More specifically, this quantum is considered to be the carrier of hermeneutical force. It arises as a field property at the complex, horizontal membrane-manifold linking human consciousness with different levels of scale of reality. When taken collectively, the aforementioned set of equations gives expression to the structural character of hermeneutical field theory. Therefore, when one begins to run concrete variables through the theory underlying these equations, one encounters various kinds of hermeneutical constraints and degrees of freedom. These constraints and degrees of freedom characterize the dialectical engagement of consciousness and reality as one seeks to acquire understanding concerning the above mentioned variables and the context which gives rise to them. Hermeneutical field theory is really the study of the factors that affect the state of the six internal
New dynamical mean-field dynamo theory and closure approach.
Blackman, Eric G; Field, George B
2002-12-23
We develop a new nonlinear mean field dynamo theory that couples field growth to the time evolution of the magnetic helicity and the turbulent electromotive force, E. We show that the difference between kinetic and current helicities emerges naturally as the growth driver when the time derivative of E is coupled into the theory. The solutions predict significant field growth in a kinematic phase and a saturation rate/strength that is magnetic Reynolds number dependent/independent in agreement with numerical simulations. The amplitude of early time oscillations provides a diagnostic for the closure.
Cold atom simulation of interacting relativistic quantum field theories.
Cirac, J Ignacio; Maraner, Paolo; Pachos, Jiannis K
2010-11-05
We demonstrate that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems. We illustrate this with two examples defined in two spacetime dimensions. The first one is the self-interacting Thirring model. The second one is a model of Dirac fermions coupled to a dynamic scalar field that gives rise to the Gross-Neveu model. The proposed cold atom experiments can be used to probe spectral or correlation properties of interacting quantum field theories thereby presenting an alternative to lattice gauge theory simulations.
Symmetries in Three-Dimensional Superconformal Quantum Field Theories
NASA Astrophysics Data System (ADS)
Bashkirov, Denis
Many examples of gauge-gravity duality and quantum equivalences of different-looking three-dimensional Quantum Field Theories indicate the existence of continuous symmetries whose currents are not built from elementary, or perturbative, fields used to write down the Lagrangian. These symmetries are called hidden or nonperturbative. We describe a method for studying continuous symmetries in a large class of three-dimensional supersymmetric gauge theories which, in particular, enables one to explore nonperturbative global symmetries and supersymmetries. As an application of the method, we prove conjectured supersymmetry enhancement in strongly coupled ABJM theory from N = 6 to N = 8 and find additional nonperturbative evidence for its duality to the N = 8 U(N) SYM theory for the minimal value of the Chern-Simons coupling. Hidden supersymmetry is also shown to occur in N = 4 d = 3 SQCD with one fundamental and one adjoint hypermultiplets. An infinite family of N = 6 d = 3 ABJ theories is proved to have hidden N = 8 superconformal symmetry and hidden parity on the quantum level. We test several conjectural dualities between ABJ theories and theories proposed by Bagger and Lambert, and Gustavsson by comparing superconformal indices of these theories. Comparison of superconformal indices is also used to test dualities between N = 2 d = 3 theories proposed by Aharony, the analysis of whose chiral rings teaches some general lessons about nonperturbative chiral operators of strongly coupled 3d supersymmetric gauge theories. As another application of our method we consider examples of hidden global symmetries in a class of quiver three-dimensional N = 4 superconformal gauge theories. Finally, we point out to the relations between some basic propeties of superconformal N ≥ 6 theories and their symmetries. The results presented in this thesis were obtained in a series of papers [1, 2, 3, 4, 5].
Massive basketball diagram for a thermal scalar field theory
NASA Astrophysics Data System (ADS)
Andersen, Jens O.; Braaten, Eric; Strickland, Michael
2000-08-01
The ``basketball diagram'' is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field with a φ4 interaction to three-loop order.
Renormalization and non-linear symmetries in quantum field theory
NASA Astrophysics Data System (ADS)
Velenich, Andrea
Most of the phenomena we experience, from the microscopic world to the universe at its largest scales, are out of equilibrium and their comprehensive formalization is one of the open problems in theoretical physics. Fluids of interacting particles cooled down or compressed quickly enough to become amorphous solids are an example of rich out-of-equilibrium systems with very slow relaxation dynamics. Even though the equilibrium phases are ordered, these systems remain trapped in glassy metastable states, with disordered microscopic structures. As a realistic model of this phenomenology, in the first part of this work I focused on a field theory of particles obeying a Brownian dynamics. The field-theoretic action displays a time-reversal symmetry leading to Fluctuation-Dissipation relations. For non-interacting particles I solved the field theory exactly, providing the explicit form of all the correlation functions, with their space and time dependence. As a non-perturbative result, the distribution of the density field has been proven to be Poissonian and not Gaussian. For interacting particles the field theory presents two major challenges: its apparent non-renormalizability and a non-linear implementation of the time-reversal symmetry. Non-linear field redefinitions can be used to make the symmetry linear and might even lead to the solution of the interacting equations of motion. However they also alter the renormalizability properties of a field theory. These challenges inspired the second part of the work, where a more abstract approach was taken. Using algebraic methods I investigated the effect of non-linear field redefinitions both on symmetry and on renormalization by focusing on simple scalar field theories as toy models. In the formal setting of the Hopf algebra of Feynman diagrams, symmetries take the form of Hopf ideals and enforce relations among scattering amplitudes; such relations can drastically reduce the number of independent couplings in a field
Improved renormalization group theory for critical asymmetry of fluids.
Wang, Long; Zhao, Wei; Wu, Liang; Li, Liyan; Cai, Jun
2013-09-28
We develop an improved renormalization group (RG) approach incorporating the critical vapor-liquid equilibrium asymmetry. In order to treat the critical asymmetry of vapor-liquid equilibrium, the integral measure is introduced in the Landau-Ginzbug partition function to achieve a crossover between the local order parameter in Ising model and the density of fluid systems. In the implementation of the improved RG approach, we relate the integral measure with the inhomogeneous density distribution of a fluid system and combine the developed method with SAFT-VR (statistical associating fluid theory of variable range) equation of state. The method is applied to various fluid systems including square-well fluid, square-well dimer fluid and real fluids such as methane (CH4), ethane (C2H6), trifluorotrichloroethane (C2F3Cl3), and sulfur hexafluoride (SF6). The descriptions of vapor-liquid equilibria provided by the developed method are in excellent agreement with simulation and experimental data. Furthermore, the improved method predicts accurate and qualitatively correct behavior of coexistence diameter near the critical point and produces the non-classical 3D Ising criticality.
Relating the archetypes of logarithmic conformal field theory
NASA Astrophysics Data System (ADS)
Creutzig, Thomas; Ridout, David
2013-07-01
Logarithmic conformal field theory is a rich and vibrant area of modern mathematical physics with well-known applications to both condensed matter theory and string theory. Our limited understanding of these theories is based upon detailed studies of various examples that one may regard as archetypal. These include the c=-2 triplet model, the Wess-Zumino-Witten model on SL(2;R) at level k=-1/2 >, and its supergroup analogue on GL(1|1). Here, the latter model is studied algebraically through representation theory, fusion and modular invariance, facilitating a subsequent investigation of its cosets and extended algebras. The results show that the archetypes of logarithmic conformal field theory are in fact all very closely related, as are many other examples including, in particular, the SL(2|1) models at levels 1 and -1/2 >. The conclusion is then that the archetypal examples of logarithmic conformal field theory are practically all the same, so we should not expect that their features are in any way generic. Further archetypal examples must be sought.
Carlson, Rebecca K; Li Manni, Giovanni; Sonnenberger, Andrew L; Truhlar, Donald G; Gagliardi, Laura
2015-01-13
Kohn-Sham density functional theory, resting on the representation of the electronic density and kinetic energy by a single Slater determinant, has revolutionized chemistry, but for open-shell systems, the Kohn-Sham Slater determinant has the wrong symmetry properties as compared to an accurate wave function. We have recently proposed a theory, called multiconfiguration pair-density functional theory (MC-PDFT), in which the electronic kinetic energy and classical Coulomb energy are calculated from a multiconfiguration wave function with the correct symmetry properties, and the rest of the energy is calculated from a density functional, called the on-top density functional, that depends on the density and the on-top pair density calculated from this wave function. We also proposed a simple way to approximate the on-top density functional by translation of Kohn-Sham exchange-correlation functionals. The method is much less expensive than other post-SCF methods for calculating the dynamical correlation energy starting with a multiconfiguration self-consistent-field wave function as the reference wave function, and initial tests of the theory were quite encouraging. Here, we provide a broader test of the theory by applying it to bond energies of main-group molecules and transition metal complexes, barrier heights and reaction energies for diverse chemical reactions, proton affinities, and the water dimerization energy. Averaged over 56 data points, the mean unsigned error is 3.2 kcal/mol for MC-PDFT, as compared to 6.9 kcal/mol for Kohn-Sham theory with a comparable density functional. MC-PDFT is more accurate on average than complete active space second-order perturbation theory (CASPT2) for main-group small-molecule bond energies, alkyl bond dissociation energies, transition-metal-ligand bond energies, proton affinities, and the water dimerization energy.
Quantum Field Theory in Curved Spacetime
NASA Astrophysics Data System (ADS)
Reynolds, Sally C.; Gallagher, Andrew
2012-03-01
List of contributors; Foreword J. T. Francis Thackeray; 1. African genesis: an evolving paradigm Sally C. Reynolds; 2. Academic genealogy Peter Ungar and Phillip V. Tobias; Part I. In Search of Origins: Evolutionary Theory, New Species, and Paths into the Past: 3. Speciation in hominin evolution Colin Groves; 4. Searching for a new paradigm for hominid origins in Chad (Central Africa) Michel Brunet; 5. From hominoid arboreality to hominid bipedalism Brigitte Senut; 6. Orrorin and the African ape/hominid dichotomy Martin Pickford; 7. A brief history and results of 40 years of Sterkfontein excavations Ronald J. Clarke; Part II. Hominin Morphology Through Time: Brains, Bodies and Teeth: 8. Hominin brain evolution, 1925-2011: an emerging overview Dean Falk; 9. The issue of brain reorganisation in Australopithecus and early hominids: Dart had it right Ralph L. Holloway; 10. The mass of the human brain: is it a spandrel? Paul R. Manger, Jason Hemingway, Muhammad Spocter and Andrew Gallagher; 11. Origin and diversity of early hominin bipedalism Henry M. McHenry; 12. Forelimb adaptations in Australopithecus afarensis Michelle S. M. Drapeau; 13. Hominin proximal femur morphology from the Tugen Hills to Flores Brian G. Richmond and William L. Jungers; 14. Daily rates of dentine formation and root extension rates in Paranthropus boisei, KNM-ER 1817, from Koobi Fora, Kenya M. Christopher Dean; 15. On the evolutionary development of early hominid molar teeth and the Gondolin Paranthropus molar Kevin L. Kuykendall; 16. Digital South African fossils: morphological studies using reference-based reconstruction and electronic preparation Gerhard W. Weber, Philipp Gunz, Simon Neubauer, Philipp Mitteroecker and Fred L. Bookstein; Part III. Modern Human Origins: Patterns, and Processes: 17. Body size in African Middle Pleistocene Homo Steven E. Churchill, Lee R. Berger, Adam Hartstone-Rose and Headman Zondo; 18. The African origin of recent humanity Milford H. Wolpoff and Sang-Hee Lee
Janiszewski, Stefan; Karch, Andreas
2013-02-22
We argue that generic nonrelativistic quantum field theories with a holographic description are dual to Hořava gravity. We construct explicit examples of this duality embedded in string theory by starting with relativistic dual pairs and taking a nonrelativistic scaling limit.
Thermofield dynamics extension of the open string field theory
NASA Astrophysics Data System (ADS)
Botta Cantcheff, M.; Scherer Santos, R. J.
2016-03-01
We study the application of the rules of thermofield dynamics (TFD) to the covariant formulation of open-string field theory. We extend the states space and fields according to the duplication rules of TFD and construct the corresponding classical action. The result is interpreted as a theory whose fields would encode the statistical information of open strings. The physical spectrum of the free theory is studied through the cohomology of the extended Becchi, Rouet, Stora and Tyutin (BRST) charge, and, as a result, we get new fields in the spectrum emerging by virtue of the quantum entanglement, and, noticeably, it presents degrees of freedom that could be identified as those of closed strings. We also show, however, that their appearing in the action is directly related to the choice of the inner product in the extended algebra, so that different sectors of fields could be eliminated from the theory by choosing that product conveniently. Finally, we study the extension of the three-vertex interaction and provide a simple prescription for it of which the results at tree level agree with those of the conventional theory.
More is the Same; Phase Transitions and Mean Field Theories
NASA Astrophysics Data System (ADS)
Kadanoff, Leo P.
2009-12-01
This paper is the first in a series that will look at the theory of phase transitions from the perspectives of physics and the philosophy of science. The series will consider a group of related concepts derived from condensed matter and statistical physics. The key technical ideas go under the names of "singularity", "order parameter", "mean field theory", "variational method", "correlation length", "universality class", "scale changes", and "renormalization". The first four of these will be considered here. In a less technical vein, the question here is how can matter, ordinary matter, support a diversity of forms. We see this diversity each time we observe ice in contact with liquid water or see water vapor (steam) come up from a pot of heated water. Different phases can be qualitatively different in that walking on ice is well within human capacity, but walking on liquid water is proverbially forbidden to ordinary humans. These differences have been apparent to humankind for millennia, but only brought within the domain of scientific understanding since the 1880s. A phase transition is a change from one behavior to another. A first order phase transition involves a discontinuous jump in some statistical variable. The discontinuous property is called the order parameter. Each phase transition has its own order parameter. The possible order parameters range over a tremendous variety of physical properties. These properties include the density of a liquid-gas transition, the magnetization in a ferromagnet, the size of a connected cluster in a percolation transition, and a condensate wave function in a superfluid or superconductor. A continuous transition occurs when the discontinuity in the jump approaches zero. This article is about statistical mechanics and the development of mean field theory as a basis for a partial understanding of phase transition phenomena. Much of the material in this review was first prepared for the Royal Netherlands Academy of Arts and
Two-Element Generation of Unitary Groups Over Finite Fields
2013-01-31
like to praise my Lord and Savior, Jesus Christ , for allowing me this opportunity to work on a Ph.D in mathematics, and for His sustaining grace...Ishibashi’s original result. The paper’s main theorem will show that all unitary groups over finite fields of odd characteristic are generated by only two
Super-Group Field Cosmology in Batalin-Vilkovisky Formulation
NASA Astrophysics Data System (ADS)
Upadhyay, Sudhaker
2016-09-01
In this paper we study the third quantized super-group field cosmology, a model in multiverse scenario, in Batalin-Vilkovisky (BV) formulation. Further, we propose the superfield/super-antifield dependent BRST symmetry transformations. Within this formulation we establish connection between the two different solutions of the quantum master equation within the BV formulation.
Ordinary versus PT-symmetric Φ³ quantum field theory
Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele
2012-04-02
A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric igΦ³ quantum field theory. This quantum fieldmore » theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p²+ix³, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian gΦ³ quantum field theory with those of the PT-symmetric igΦ³ quantum field theory. It is shown that while the conventional gΦ³ theory in d=6 dimensions is asymptotically free, the igΦ³ theory is like a gΦ⁴ theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.« less
World sheet commuting {beta}{gamma} conformal field theory and nonrelativistic string theories
Kim, Bom Soo
2007-11-15
We construct a sigma model in two dimensions with Galilean symmetry in flat target space similar to the sigma model of the critical string theory with Lorentz symmetry in 10 flat spacetime dimensions. This is motivated by the works of Gomis and Ooguri [J. Math. Phys. (N.Y.) 42, 3127 (2001)] and Danielsson et al. [J. High Energy Phys. 10 (2000) 020; J. High Energy Phys. 03 (2001) 041.]. Our theory is much simpler than their theory and does not assume a compact coordinate. This nonrelativistic string theory has a bosonic matter {beta}{gamma} conformal field theory with the conformal weight of {beta} as 1. It is natural to identify time as a linear combination of {gamma} and {gamma} through an explicit realization of the Galilean boost symmetry. The angle between {gamma} and {gamma} parametrizes one parameter family of selection sectors. These selection sectors are responsible for having a nonrelativistic dispersion relation without a nontrivial topology in the nonrelativistic setup, which is one of the major differences from the previous works of Gomis and Ooguri and of Danielsson and co-workers. This simple theory is the nonrelativistic analogue of the critical string theory, and there are many different avenues ahead to be investigated. We mention a possible consistent generalization of this theory with different conformal weights for the {beta}{gamma} conformal field theory. We also mention supersymmetric generalizations of these theories.
Quantum field theory in spaces with closed timelike curves
NASA Astrophysics Data System (ADS)
Boulware, David G.
1992-11-01
Gott spacetime has closed timelike curves, but no locally anomalous stress energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 2π. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the noncausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the noncausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
IAU Working Group on Wide-Field Imaging.
NASA Astrophysics Data System (ADS)
MacGillivray, H. T.
1991-01-01
Contents: 1. Introduction - The IAU Working Group on Wide-Field Imaging (R. M. West). 2. Reports from the Sub-Sections of the Working Group - a. Sky surveys and patrols (R. M. West). b. Photographic techniques (D. F. Malin). c. Digitization techniques (H. T. MacGillivray). d. Archival and retrieval of wide-field data (B. Lasker). 3. Meeting of the Organising Committee (R. M. West). 4. Wide-field plate archives (M. Tsvetkov). 5. Reproduction of the Palomar Observatory Sky Surveys (R. J. Brucato). 6. Status of the St ScI scan-distribution program (B. Lasker). 7. Pixel addition - pushing Schmidt plates to B = 25 (M. R. S. Hawkins). 8. Photometry from Estar film (S. Phillipps, Q. Parker). 9. ASCHOT - Astrophysical Schmidt Orbital Telescope (H. Lorenz). 10. The Hitchhiker parallel CCD camera (J. Davies, M. Disney, S. Driver, I. Morgan, S. Phillipps).
Effective field theories for QCD with rooted staggered fermions
Bernard, Claude; Golterman, Maarten; Shamir, Yigal
2008-04-01
Even highly improved variants of lattice QCD with staggered fermions show significant violations of taste symmetry at currently accessible lattice spacings. In addition, the 'rooting trick' is used in order to simulate with the correct number of light sea quarks, and this makes the lattice theory nonlocal, even though there is good reason to believe that the continuum limit is in the correct universality class. In order to understand scaling violations, it is thus necessary to extend the construction of the Symanzik effective theory to include rooted staggered fermions. We show how this can be done, starting from a generalization of the renormalization-group approach to rooted staggered fermions recently developed by one of us. We then explain how the chiral effective theory follows from the Symanzik action, and show that it leads to 'rooted' staggered chiral perturbation theory as the correct chiral theory for QCD with rooted staggered fermions. We thus establish a direct link between the renormalization-group based arguments for the correctness of the continuum limit and the success of rooted staggered chiral perturbation theory in fitting numerical results obtained with the rooting trick. In order to develop our argument, we need to assume the existence of a standard partially-quenched chiral effective theory for any local partially-quenched theory. Other technical, but standard, assumptions are also required.
SL(2, z) Action on Three-Dimensional Conformal Field Theories with Abelian Symmetry
NASA Astrophysics Data System (ADS)
Witten, Edward
On the space of three-dimensional conformal field theories with U(1) symmetry and a chosen coupling to a background gauge field, there is a natural action of the group SL(2, Z). The generator S of SL(2, Z) acts by letting the background gauge field become dynamical, an operation considered recently by Kapustin and Strassler in explaining three-dimensional mirror symmetry. The other generator T acts by shifting the Chern-Simons coupling of the background field. This SL(2, Z) action in three dimensions is related by the AdS/CFT correspondence to SL(2, Z) duality of low energy U(1) gauge fields in four dimensions.
Inductive approach towards a phenomenologically more satisfactory unififed field theory
Rayski, J.; Rayski J.M. Jnr.
1985-11-01
A unified field theory constituting a fusion of the ideas of supersymmetries with general relativity and gauge theory is investigated. A Lagrangian formalism is constructed step by step; the last step consists in a marriage with Kaluza's idea of a multidimensional space-time. Our aim is not to achieve a full local supersymmetry in eleven dimensions, but rather to attain a compromise with the symmetries of the fundamental interactions either known phenomenologically, or only suspected to exist in nature.
Theory of Near-Field Scanning with a Probe Array
2014-01-01
NF samples are then processed to produce FF patterns. The processing, known as the NF-to-FF transformation [1][2], is exact and rigorous in that, if...location and is a critical input to the NF-to-FF transformation . The expansion coefficients b(−) of the total outgoing field determines the extent of...of error, we provided a probe array compensation theory based on the Lorentz reciprocity theorem [29]. The theory permits expression of the open
Large field inflation models from higher-dimensional gauge theories
NASA Astrophysics Data System (ADS)
Furuuchi, Kazuyuki; Koyama, Yoji
2015-02-01
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante's Inferno model turns out to be the most preferred model in this framework.
Quantum field theory on curved spacetimes: Axiomatic framework and examples
NASA Astrophysics Data System (ADS)
Fredenhagen, Klaus; Rejzner, Kasia
2016-03-01
In this review article, we want to expose a systematic development of quantum field theory on curved spacetimes. The leading principle is the emphasis on local properties. It turns out that this requires a reformulation of the QFT framework which also yields a new perspective for the theories on Minkowski space. The aim of the present work is to provide an almost self-contained introduction into the framework, which should be accessible for both mathematical physicists and mathematicians.
Chiral Effective Field Theory in the $\\Delta$-resonance region
Vladimir Pascalutsa
2006-09-18
I discuss the problem of constructing an effective low-energy theory in the vicinity of a resonance or a bound state. The focus is on the example of the $\\Delta(1232)$, the lightest resonance in the nucleon sector. Recent developments of the chiral effective-field theory in the $\\Delta$-resonance region are briefly reviewed. I conclude with a comment on the merits of the manifestly covariant formulation of chiral EFT in the baryon sector.
Large field inflation models from higher-dimensional gauge theories
Furuuchi, Kazuyuki; Koyama, Yoji
2015-02-23
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante’s Inferno model turns out to be the most preferred model in this framework.
Motion of small bodies in classical field theory
Gralla, Samuel E.
2010-04-15
I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body's composition (and, e.g., black holes are allowed). The worldline 'left behind' by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the 'Bianchi identity' for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the ''monopoles'' of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of 'chameleon' bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.
Quantum Lifshitz Field Theory of a Frustrated Ferromagnet.
Balents, Leon; Starykh, Oleg A
2016-04-29
We propose a universal nonlinear sigma model field theory for one-dimensional frustrated ferromagnets, which applies in the vicinity of a "quantum Lifshitz point," at which the ferromagnetic state develops a spin wave instability. We investigate the phase diagram resulting from perturbations of the exchange and of magnetic field away from the Lifshitz point, and uncover a rich structure with two distinct regimes of different properties, depending upon the value of a marginal, dimensionless, parameter of the theory. In the regime relevant for one-dimensional systems with low spin, we find a metamagnetic transition line to a vector chiral phase. This line terminates in a critical end point, beyond which there is at least one multipolar or "spin nematic" phase. We show that the field theory is asymptotically exactly soluble near the Lifshitz point.
Quantum entanglement of local operators in conformal field theories.
Nozaki, Masahiro; Numasawa, Tokiro; Takayanagi, Tadashi
2014-03-21
We introduce a series of quantities which characterize a given local operator in any conformal field theory from the viewpoint of quantum entanglement. It is defined by the increased amount of (Rényi) entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in two, four and six dimensions. We find that these results are interpreted in terms of quantum entanglement of a finite number of states, including Einstein-Podolsky-Rosen states. They agree with a heuristic picture of propagations of entangled particles.
Quantum Entanglement of Local Operators in Conformal Field Theories
NASA Astrophysics Data System (ADS)
Nozaki, Masahiro; Numasawa, Tokiro; Takayanagi, Tadashi
2014-03-01
We introduce a series of quantities which characterize a given local operator in any conformal field theory from the viewpoint of quantum entanglement. It is defined by the increased amount of (Rényi) entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in two, four and six dimensions. We find that these results are interpreted in terms of quantum entanglement of a finite number of states, including Einstein-Podolsky-Rosen states. They agree with a heuristic picture of propagations of entangled particles.
A Variational Statistical-Field Theory for Polar Liquid Mixtures
NASA Astrophysics Data System (ADS)
Zhuang, Bilin; Wang, Zhen-Gang
Using a variational field-theoretic approach, we derive a molecularly-based theory for polar liquid mixtures. The resulting theory consists of simple algebraic expressions for the free energy of mixing and the dielectric constant as functions of mixture composition. Using only the dielectric constants and the molar volumes of the pure liquid constituents, the theory evaluates the mixture dielectric constants in good agreement with the experimental values for a wide range of liquid mixtures, without using adjustable parameters. In addition, the theory predicts that liquids with similar dielectric constants and molar volumes dissolve well in each other, while sufficient disparity in these parameters result in phase separation. The calculated miscibility map on the dielectric constant-molar volume axes agrees well with known experimental observations for a large number of liquid pairs. Thus the theory provides a quantification for the well-known empirical ``like-dissolves-like'' rule. Bz acknowledges the A-STAR fellowship for the financial support.
Continuous-spin particle field theory with helicity correspondence
NASA Astrophysics Data System (ADS)
Schuster, Philip; Toro, Natalia
2015-01-01
We propose the first covariant local action describing the propagation of a single free continuous-spin degree of freedom. The theory is simply formulated as a gauge theory in a "vector superspace," but can also be formulated in terms of a tower of symmetric tensor gauge fields. When the spin invariant ρ vanishes, the helicity correspondence is manifest—familiar gauge theory actions are recovered and couplings to conserved currents can easily be introduced. For nonzero ρ , a tower of tensor currents must be present, of which only the lowest rank is exactly conserved. A paucity of local gauge-invariant operators for nonzero ρ suggests that the equations of motion in any interacting theory should be covariant, not invariant, under a generalization of the free theory's gauge symmetry.
NASA Astrophysics Data System (ADS)
Nakayama, Yu
2017-02-01
We show that 11-dimensional supergravity in Euclidean signature admits an exact classical solution with isometry corresponding to a three-dimensional scale-invariant field theory without conformal invariance. We also construct the holographic renormalization group flow that connects the known UV conformal fixed point and the new scale-invariant but not conformal fixed point. In view of holography, the existence of such classical solutions suggests that the topologically twisted M2-brane gauge theory possesses a scale-invariant but not conformal phase.
Entanglement entropy of non-unitary conformal field theory
NASA Astrophysics Data System (ADS)
Bianchini, D.; Castro-Alvaredo, O.; Doyon, B.; Levi, E.; Ravanini, F.
2015-01-01
Here we show that the Rényi entanglement entropy of a region of large size ℓ in a one-dimensional critical model whose ground state breaks conformal invariance (such as in those described by non-unitary conformal field theories), behaves as {{S}n}˜ \\frac{{{c}eff}(n+1)}{6n}log \\ell , where {{c}eff}=c-24Δ \\gt 0 is the effective central charge, c (which may be negative) is the central charge of the conformal field theory and Δ \
Global Symmetries, Volume Independence, and Continuity in Quantum Field Theories.
Sulejmanpasic, Tin
2017-01-06
We discuss quantum field theories with global SU(N) and O(N) symmetries for which temporal direction is compactified on a circle of size L with periodicity of fields up to a global symmetry transformation, i.e., twisted boundary conditions. Such boundary conditions correspond to an insertion of the global symmetry operator in the partition function. We argue in general and prove in particular for CP(N-1) and O(N) nonlinear sigma models that large-N volume independence holds. Further we show that the CP(N-1) theory is free from the Affleck phase transition confirming the Ünsal-Dunne continuity conjecture.
Mapping a Massless Scalar Field Theory on a Yang-Mills Theory:. Classical Case
NASA Astrophysics Data System (ADS)
Frasca, Marco
We analyze a recent proposal to map a massless scalar field theory onto a Yang-Mills theory at classical level. It is seen that this mapping exists at a perturbative level when the expansion is a gradient expansion. In this limit the theories share the spectrum, at the leading order, that is the one of a harmonic oscillator. Gradient expansion is exploited maintaining Lorentz covariance by introducing a fifth coordinate and turning the theory to Euclidean space. These expansions give common solutions to scalar and Yang-Mills field equations that are so proved to exist by construction, confirming that the selected components of the Yang-Mills field are indeed an extremum of the corresponding action functional.
A field theory of piezoelectric media containing dislocations
Taupin, V. Fressengeas, C.; Ventura, P.; Lebyodkin, M.
2014-04-14
A field theory is proposed to extend the standard piezoelectric framework for linear elastic solids by accounting for the presence and motion of dislocation fields and assessing their impact on the piezoelectric properties. The proposed theory describes the incompatible lattice distortion and residual piezoelectric polarization fields induced by dislocation ensembles, as well as the dynamic evolution of these fields through dislocation motion driven by coupled electro-mechanical loading. It is suggested that (i) dislocation mobility may be enhanced or inhibited by the electric field, depending on the polarity of the latter, (ii) plasticity mediated by dislocation motion allows capturing long-term time-dependent properties of piezoelectric polarization. Due to the continuity of the proposed electro-mechanical framework, the stress/strain and polarization fields are smooth even in the dislocation core regions. The theory is applied to gallium nitride layers for validation. The piezoelectric polarization fields associated with bulk screw/edge dislocations are retrieved and surface potential modulations are predicted. The results are extended to dislocation loops.
Preheating in an asymptotically safe quantum field theory
NASA Astrophysics Data System (ADS)
Svendsen, Ole; Moghaddam, Hossein Bazrafshan; Brandenberger, Robert
2016-10-01
We consider reheating in a class of asymptotically safe quantum field theories recently studied in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J. High Energy Phys. 01 (2016) 081]. These theories allow for an inflationary phase in the very early universe. Inflation ends with a period of reheating. Since the models contain many scalar fields which are intrinsically coupled to the inflaton there is the possibility of parametric resonance instability in the production of these fields, and the danger that the induced curvature fluctuations will become too large. Here we show that the parametric instability indeed arises, and that hence the energy transfer from the inflaton condensate to fluctuating fields is rapid. Demanding that the curvature fluctuations induced by the parametrically amplified entropy modes do not exceed the upper observational bounds puts a lower bound on the number of fields which the model followed in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, J. High Energy Phys. 01 (2016) 081] must contain. This bound also depends on the total number of e -foldings of the inflationary phase.
Quantum field theory with a preferred direction: The very special relativity framework
NASA Astrophysics Data System (ADS)
Lee, Cheng-Yang
2016-02-01
The theory of very special relativity (VSR) proposed by Cohen and Glashow contains an intrinsic preferred direction. Starting from the irreducible unitary representation of the inhomogeneous VSR group I S I M (2 ), we present a rigorous construction of quantum field theory with a preferred direction. We find that although the particles and their quantum fields between the VSR and Lorentz sectors are physically different, they share many similarities. The massive spin-half and spin-one vector fields are local and satisfy the Dirac and Proca equations, respectively. This result can be generalized to higher-spin field theories. By studying the Yukawa and standard gauge interactions, we obtain a qualitative understanding on the effects of the preferred direction. Its effect is manifest for polarized processes but are otherwise absent.
Renormalization-group theory for the eddy viscosity in subgrid modeling
NASA Technical Reports Server (NTRS)
Zhou, YE; Vahala, George; Hossain, Murshed
1988-01-01
Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.
NASA Astrophysics Data System (ADS)
Oh, Jae-Hyuk
2016-11-01
We explore the mathematical relation between stochastic quantization (SQ) and the holographic Wilsonian renormalization group (HWRG) of a massive scalar field defined in asymptotically anti-de Sitter space. We compute the stochastic two-point correlation function by quantizing the boundary on-shell action (it is identified with the Euclidean action in our stochastic frame) of the scalar field, requiring the initial value of the stochastic field Dirichlet boundary condition, and study its relationship with the double-trace deformation in HWRG computation. It turns out that the stochastic two-point function precisely corresponds to the double-trace deformation through the relation proposed in [J. High Energy Phys. 11 (2012) 144] even in the case that the scalar field mass is arbitrary. In our stochastic framework, the Euclidean action constituting the Langevin equation is not the same as that in the original stochastic theory; in fact, it contains the stochastic time "t -dependent" kernel in it. A justification for the exotic Euclidean action is provided by proving that it transforms to the usual form of the Euclidean action in a new stochastic frame by an appropriate rescaling of both the stochastic fields and time. We also apply the Neumann boundary condition to the stochastic fields to study the relation between SQ and the HWRG when alternative quantization is allowed. It turns out that the application of the Neumann boundary condition to the stochastic fields generates the radial evolution of the single-trace operator as well as the double-trace term.
Soto, Ana M.; Sonnenschein, Carlos
2014-01-01
The somatic mutation theory (SMT) of cancer has been and remains the prevalent theory attempting to explain how neoplasms arise and progress. This theory proposes that cancer is a clonal, cell-based disease, and implicitly assumes that quiescence is the default state of cells in multicellular organisms. The SMT has not been rigorously tested, and several lines of evidence raise questions that are not addressed by this theory. Herein, we propose experimental strategies that may validate the SMT. We also call attention to an alternative theory of carcinogenesis, the tissue organization field theory (TOFT), which posits that cancer is a tissue-based disease and that proliferation is the default state of all cells. Based on epistemological and experimental evidence, we argue that the TOFT compellingly explains carcinogenesis, while placing it within an evolutionarily relevant context. PMID:21503935
Lattice field theory studies of magnetic catalysis in graphene
NASA Astrophysics Data System (ADS)
Winterowd, Christopher R.
Consisting of a single two-dimensional layer of Carbon atoms arranged in a hexagonal lattice, graphene represents one of the most exciting recent developments in condensed matter physics. With novel electronic and mechancial properties, graphene not only has great potential with respect to technological applications, but also displays phenomena that typically appear in relativistic quantum field theory. The low-energy electronic excitations of graphene consist of two identical species of massless Dirac particles. Due to the small Fermi velocity, these particles are strongly coupled through the Coulomb interaction. Although various perturbative approaches have succeeded in elucidating many of the electronic properties of graphene, one would still like a nonperturbative study to address various questions. In particular, the spontaneous breaking of chiral symmetry in the presence of an external magnetic field, commonly known as magnetic catalysis, is one of these questions. Early studies of this phenomenon in model relativistic field theories have posited the mechanism to be universal. More recently, this mechanism of spontaneous symmetry breaking has been studied in low-dimensional condensed matter systems. Due to the strongly-coupled nature of the low-energy effective field theory of graphene, nonperturbative methods of lattice gauge theory can be used which are well suited to studying chiral symmetry breaking. Most notably used to study the theory of the strong interactions, quantum chromodynamics, these methods have proven successful in elucidating nonperturbative phenomena in cases where perturbative methods fail. In this thesis, using these methods, evidence in favor of magnetic catalysis in the graphene effective field theory will be presented.
Fuzzy Field Theory as a Random Matrix Model
NASA Astrophysics Data System (ADS)
Tekel, Juraj
This dissertation considers the theory of scalar fields on fuzzy spaces from the point of view of random matrices. First we define random matrix ensembles, which are natural description of such theory. These ensembles are new and the novel feature is a presence of kinetic term in the probability measure, which couples the random matrix to a set of external matrices and thus breaks the original symmetry. Considering the case of a free field ensemble, which is generalization of a Gaussian matrix ensemble, we develop a technique to compute expectation values of the observables of the theory based on explicit Wick contractions and we write down recursion rules for these. We show that the eigenvalue distribution of the random matrix follows the Wigner semicircle distribution with a rescaled radius. We also compute distributions of the matrix Laplacian of the random matrix given by the new term and demonstrate that the eigenvalues of these two matrices are correlated. We demonstrate the robustness of the method by computing expectation values and distributions for more complicated observables. We then consider the ensemble corresponding to an interacting field theory, with a quartic interaction. We use the same method to compute the distribution of the eigenvalues and show that the presence of the kinetic terms rescales the distribution given by the original theory, which is a polynomially deformed Wigner semicircle. We compute the eigenvalue distribution of the matrix Laplacian and the joint distribution up to second order in the correlation and we show that the correlation between the two changes from the free field case. Finally, as an application of these results, we compute the phase diagram of the fuzzy scalar field theory, we find multiscaling which stabilizes this diagram in the limit of large matrices and compare it with the results obtained numerically and by considering the kinetic part as a perturbation.
Field theory of propagating reaction-diffusion fronts
Escudero, C.
2004-10-01
The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean-field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to be taken into account. Here, we construct an analytic theory connecting the first principles of the reaction-diffusion process to an effective equation of motion via field-theoretic arguments, and we arrive at results already confirmed by numerical simulations.
Topological BF field theory description of topological insulators
Cho, Gil Young; Moore, Joel E.
2011-06-15
Research Highlights: > We show that a BF theory is the effective theory of 2D and 3D topological insulators. > The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. > The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. > Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a {pi} flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.
Aspects of Supersymmetric Field Theories and Complex Geometry
NASA Astrophysics Data System (ADS)
Crichigno, Patricio Marcos
In this dissertation we study various aspects of Supersymmetric Quantum Field Theory and Complex Geometry. We focus on three main aspects. The first is general N = (2, 2) gauged linear sigma models involving semichiral fields. We show that integrating out the semichiral vector multiplet leads to the generalized potential for a hyperkahler manifold, providing a formulation of the hyperkahler quotient in a generalized setting. We then discuss a new quotient construction which leads to non-Kahler manifolds. The second problem we study is motivated by recent developments in the study of the Coulomb branch of supersymmetric theories with a hyperkahler moduli space. A crucial element in these developments is the expression for Darboux coordinates in the hyperkahler manifold. We give a simple derivation of this expression by using projective superspace techniques and we apply this to the study of the moduli space of theories with eight supercharges on R3 x S¹ and R3 x T². Finally, we study the partition function of three-dimensional Chern-Simons theories on S³ with affine ADE quivers. We give a general formula for the partition function of affine D-type quivers in terms of the Chern-Simons levels, providing a prediction for the volume of an infinite family of tri-Sasaki Einstein manifolds corresponding to the gravitational duals of such field theories.
Dynamics of perturbations in Double Field Theory & non-relativistic string theory
NASA Astrophysics Data System (ADS)
Ko, Sung Moon; Melby-Thompson, Charles M.; Meyer, René; Park, Jeong-Hyuck
2015-12-01
Double Field Theory provides a geometric framework capable of describing string theory backgrounds that cannot be understood purely in terms of Riemannian geometry — not only globally (`non-geometry'), but even locally (`non-Riemannian'). In this work, we show that the non-relativistic closed string theory of Gomis and Ooguri [1] arises precisely as such a non-Riemannian string background, and that the Gomis-Ooguri sigma model is equivalent to the Double Field Theory sigma model of [2] on this background. We further show that the target-space formulation of Double Field Theory on this non-Riemannian background correctly reproduces the appropriate sector of the Gomis-Ooguri string spectrum. To do this, we develop a general semi-covariant formalism describing perturbations in Double Field Theory. We derive compact expressions for the linearized equations of motion around a generic on-shell background, and construct the corresponding fluctuation Lagrangian in terms of novel completely covariant second order differential operators. We also present a new non-Riemannian solution featuring Schrödinger conformal symmetry.
Positive Energy Conditions in 4D Conformal Field Theory
NASA Astrophysics Data System (ADS)
Farnsworth, Kara; Luty, Markus; Prilepina, Valentina
2016-03-01
We argue that all consistent 4D quantum field theories obey a spacetime-averaged weak energy inequality avgT00 >= - C /L4 , where L is the size of the smearing region, and C is a positive constant that depends on the theory. If this condition is violated, the theory has states that are indistinguishable from states of negative total energy by any local measurement, and we expect instabilities or other inconsistencies. We apply this condition to 4D conformal field theories, and find that it places constraints on the OPE coefficients of the theory. The constraints we find are weaker than the ``conformal collider'' constraints of Hofman and Maldacena. We speculate that there may be theories that violate the Hofman-Maldacena bounds, but satisfy our bounds. In 3D CFTs, the only constraint we find is equivalent to the positivity of 2-point function of the energy-momentum tensor, which follows from unitarity. Our calculations are performed using momentum-space Wightman functions, which are remarkably simple functions of momenta, and may be of interest in their own right.
Dirac's equation and the nature of quantum field theory
NASA Astrophysics Data System (ADS)
Plotnitsky, Arkady
2012-11-01
This paper re-examines the key aspects of Dirac's derivation of his relativistic equation for the electron in order advance our understanding of the nature of quantum field theory. Dirac's derivation, the paper argues, follows the key principles behind Heisenberg's discovery of quantum mechanics, which, the paper also argues, transformed the nature of both theoretical and experimental physics vis-à-vis classical physics and relativity. However, the limit theory (a crucial consideration for both Dirac and Heisenberg) in the case of Dirac's theory was quantum mechanics, specifically, Schrödinger's equation, while in the case of quantum mechanics, in Heisenberg's version, the limit theory was classical mechanics. Dirac had to find a new equation, Dirac's equation, along with a new type of quantum variables, while Heisenberg, to find new theory, was able to use the equations of classical physics, applied to different, quantum-mechanical variables. In this respect, Dirac's task was more similar to that of Schrödinger in his work on his version of quantum mechanics. Dirac's equation reflects a more complex character of quantum electrodynamics or quantum field theory in general and of the corresponding (high-energy) experimental quantum physics vis-à-vis that of quantum mechanics and the (low-energy) experimental quantum physics. The final section examines this greater complexity and its implications for fundamental physics.
Representing the Electromagnetic Field: How Maxwell's Mathematics Empowered Faraday's Field Theory
ERIC Educational Resources Information Center
Tweney, Ryan D.
2011-01-01
James Clerk Maxwell "translated" Michael Faraday's experimentally-based field theory into the mathematical representation now known as "Maxwell's Equations." Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other…
NASA Astrophysics Data System (ADS)
Goncharov, Yu. P.
This survey is devoted to possible manifestations of remarkable topological duality between real scalar and spinor fields (TDSS) existing on a great number of manifolds important in physical applications. The given manifestations are demonstrated to occur within the framework of miscellaneous branches in ordinary and supersymmetric quantum field theories, supergravity, Kaluza-Klein type theories, cosmology, strings, membranes and p-branes. All this allows one to draw the condusion that the above duality will seem to be an essential ingredient in many questions of present and future investigations.
An effective field theory for forward scattering and factorization violation
NASA Astrophysics Data System (ADS)
Rothstein, Ira Z.; Stewart, Iain W.
2016-08-01
Starting with QCD, we derive an effective field theory description for forward scattering and factorization violation as part of the soft-collinear effective field theory (SCET) for high energy scattering. These phenomena are mediated by long distance Glauber gluon exchanges, which are static in time, localized in the longitudinal distance, and act as a kernel for forward scattering where | t| ≪ s. In hard scattering, Glauber gluons can induce corrections which invalidate factorization. With SCET, Glauber exchange graphs can be calculated explicitly, and are distinct from graphs involving soft, collinear, or ultrasoft gluons. We derive a complete basis of operators which describe the leading power effects of Glauber exchange. Key ingredients include regulating light-cone rapidity singularities and subtractions which prevent double counting. Our results include a novel all orders gauge invariant pure glue soft operator which appears between two collinear rapidity sectors. The 1-gluon Feynman rule for the soft operator coincides with the Lipatov vertex, but it also contributes to emissions with ≥ 2 soft gluons. Our Glauber operator basis is derived using tree level and one-loop matching calculations from full QCD to both SCETII and SCETI. The one-loop amplitude's rapidity renormalization involves mixing of color octet operators and yields gluon Reggeization at the amplitude level. The rapidity renormalization group equation for the leading soft and collinear functions in the forward scattering cross section are each given by the BFKL equation. Various properties of Glauber gluon exchange in the context of both forward scattering and hard scattering factorization are described. For example, we derive an explicit rule for when eikonalization is valid, and provide a direct connection to the picture of multiple Wilson lines crossing a shockwave. In hard scattering operators Glauber subtractions for soft and collinear loop diagrams ensure that we are not sensitive to
Decoherence in an interacting quantum field theory: The vacuum case
Koksma, Jurjen F.; Prokopec, Tomislav; Schmidt, Michael G.
2010-03-15
We apply the decoherence formalism to an interacting scalar field theory. In the spirit of the decoherence literature, we consider a 'system field' and an 'environment field' that interact via a cubic coupling. We solve for the propagator of the system field, where we include the self-energy corrections due to the interaction with the environment field. In this paper, we consider an environment in the vacuum state (T=0). We show that neglecting inaccessible non-Gaussian correlators increases the entropy of the system as perceived by the observer. Moreover, we consider the effect of a changing mass of the system field in the adiabatic regime, and we find that at late times no additional entropy has been generated.
Theory of a ring laser. [electromagnetic field and wave equations
NASA Technical Reports Server (NTRS)
Menegozzi, L. N.; Lamb, W. E., Jr.
1973-01-01
Development of a systematic formulation of the theory of a ring laser which is based on first principles and uses a well-known model for laser operation. A simple physical derivation of the electromagnetic field equations for a noninertial reference frame in uniform rotation is presented, and an attempt is made to clarify the nature of the Fox-Li modes for an open polygonal resonator. The polarization of the active medium is obtained by using a Fourier-series method which permits the formulation of a strong-signal theory, and solutions are given in terms of continued fractions. It is shown that when such a continued fraction is expanded to third order in the fields, the familiar small-signal ring-laser theory is obtained.
On gradient field theories: gradient magnetostatics and gradient elasticity
NASA Astrophysics Data System (ADS)
Lazar, Markus
2014-09-01
In this work, the fundamentals of gradient field theories are presented and reviewed. In particular, the theories of gradient magnetostatics and gradient elasticity are investigated and compared. For gradient magnetostatics, non-singular expressions for the magnetic vector gauge potential, the Biot-Savart law, the Lorentz force and the mutual interaction energy of two electric current loops are derived and discussed. For gradient elasticity, non-singular forms of all dislocation key formulas (Burgers equation, Mura equation, Peach-Koehler stress equation, Peach-Koehler force equation, and mutual interaction energy of two dislocation loops) are presented. In addition, similarities between an electric current loop and a dislocation loop are pointed out. The obtained fields for both gradient theories are non-singular due to a straightforward and self-consistent regularization.
Geometric and Topological Methods for Quantum Field Theory
NASA Astrophysics Data System (ADS)
Cardona, Alexander; Contreras, Iván.; Reyes-Lega, Andrés. F.
2013-05-01
Introduction; 1. A brief introduction to Dirac manifolds Henrique Bursztyn; 2. Differential geometry of holomorphic vector bundles on a curve Florent Schaffhauser; 3. Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles Sylvie Paycha; 4. Introduction to Feynman integrals Stefan Weinzierl; 5. Iterated integrals in quantum field theory Francis Brown; 6. Geometric issues in quantum field theory and string theory Luis J. Boya; 7. Geometric aspects of the standard model and the mysteries of matter Florian Scheck; 8. Absence of singular continuous spectrum for some geometric Laplacians Leonardo A. Cano García; 9. Models for formal groupoids Iván Contreras; 10. Elliptic PDEs and smoothness of weakly Einstein metrics of Hölder regularity Andrés Vargas; 11. Regularized traces and the index formula for manifolds with boundary Alexander Cardona and César Del Corral; Index.
Holographic Duals for Five-Dimensional Superconformal Quantum Field Theories.
D'Hoker, Eric; Gutperle, Michael; Uhlemann, Christoph F
2017-03-10
We construct global solutions to type IIB supergravity with 16 residual supersymmetries whose space-time is AdS_{6}×S^{2} warped over a Riemann surface. Families of solutions are labeled by an arbitrary number L≥3 of asymptotic regions, in each of which the supergravity fields match those of a (p,q) five-brane, and may therefore be viewed as near-horizon limits of fully localized intersections of five-branes in type IIB string theory. These solutions provide compelling candidates for holographic duals to a large class of five-dimensional superconformal quantum field theories which arise as nontrivial UV fixed points of perturbatively nonrenormalizable Yang-Mills theories, thereby making them more directly accessible to quantitative analysis.
Holographic Duals for Five-Dimensional Superconformal Quantum Field Theories
NASA Astrophysics Data System (ADS)
D'Hoker, Eric; Gutperle, Michael; Uhlemann, Christoph F.
2017-03-01
We construct global solutions to type IIB supergravity with 16 residual supersymmetries whose space-time is AdS6×S2 warped over a Riemann surface. Families of solutions are labeled by an arbitrary number L ≥3 of asymptotic regions, in each of which the supergravity fields match those of a (p ,q ) five-brane, and may therefore be viewed as near-horizon limits of fully localized intersections of five-branes in type IIB string theory. These solutions provide compelling candidates for holographic duals to a large class of five-dimensional superconformal quantum field theories which arise as nontrivial UV fixed points of perturbatively nonrenormalizable Yang-Mills theories, thereby making them more directly accessible to quantitative analysis.
Information channel capacity in the field theory estimation
NASA Astrophysics Data System (ADS)
Sładkowski, J.; Syska, J.
2012-12-01
The construction of the information capacity for the vector position parameter in the Minkowskian space-time is presented. This lays the statistical foundations of the kinematical term of the Lagrangian of the physical action for many field theory models, derived by the extremal physical information method of Frieden and Soffer.
The effective field theory of K-mouflage
NASA Astrophysics Data System (ADS)
Brax, Philippe; Valageas, Patrick
2016-01-01
We describe K-mouflage models of modified gravity using the effective field theory of dark energy. We show how the Lagrangian density K defining the K-mouflage models appears in the effective field theory framework, at both the exact fully nonlinear level and at the quadratic order of the effective action. We find that K-mouflage scenarios only generate the operator (δg00(u))n at each order n. We also reverse engineer K-mouflage models by reconstructing the whole effective field theory, and the full cosmological behaviour, from two functions of the Jordan-frame scale factor in a tomographic manner. This parameterisation is directly related to the implementation of the K-mouflage screening mechanism: screening occurs when K' is large in a dense environment such as the deep matter and radiation eras. In this way, K-mouflage can be easily implemented as a calculable subclass of models described by the effective field theory of dark energy which could be probed by future surveys.
An alternative topological field theory of generalized complex geometry
NASA Astrophysics Data System (ADS)
Ikeda, Noriaki; Tokunaga, Tatsuya
2007-09-01
We propose a new topological field theory on generalized complex geometry in two dimension using AKSZ formulation. Zucchini's model is A model in the case that the generalized complex structure depends on only a symplectic structure. Our new model is B model in the case that the generalized complex structure depends on only a complex structure.
Effective field theory for plasmas at all temperatures and densities
NASA Astrophysics Data System (ADS)
Braaten, Eric
1993-05-01
The solution of the plasmon problem and the subsequent development of an effective field-theory approach to ultrarelativistic plasmas are reviewed. The effective Lagrangians that summarize collective effects in ultrarelativistic quark-gluon and electron-photon plasmas are presented. A generalization that describes an electromagnetic plasma at all temperatures and densities is proposed.
Recent Progress in Nuclear Lattice Simulations with Effective Field Theory
NASA Astrophysics Data System (ADS)
Lee, D.
2007-10-01
This proceedings article summarizes recent work presented at Chiral Dynamics 2006 on nuclear lattice simulations with chiral effective field theory for light nuclei. This work has been done in collaboration with Bubar {gra} Borasoy , Evgeny Epelbaum, Hermann Krebs, and Ulf-G. Meißner.
Constructive field theory and applications: Perspectives and open problems
NASA Astrophysics Data System (ADS)
Rivasseau, V.
2000-06-01
In this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory. They could give work for future mathematical physicists trained with constructive methods well into the 21st century.
Dynamical mean-field theory from a quantum chemical perspective.
Zgid, Dominika; Chan, Garnet Kin-Lic
2011-03-07
We investigate the dynamical mean-field theory (DMFT) from a quantum chemical perspective. Dynamical mean-field theory offers a formalism to extend quantum chemical methods for finite systems to infinite periodic problems within a local correlation approximation. In addition, quantum chemical techniques can be used to construct new ab initio Hamiltonians and impurity solvers for DMFT. Here, we explore some ways in which these things may be achieved. First, we present an informal overview of dynamical mean-field theory to connect to quantum chemical language. Next, we describe an implementation of dynamical mean-field theory where we start from an ab initio Hartree-Fock Hamiltonian that avoids double counting issues present in many applications of DMFT. We then explore the use of the configuration interaction hierarchy in DMFT as an approximate solver for the impurity problem. We also investigate some numerical issues of convergence within DMFT. Our studies are carried out in the context of the cubic hydrogen model, a simple but challenging test for correlation methods. Finally, we finish with some conclusions for future directions.
Chiral field theories as models for hadron substructure
Kahana, S.H.
1987-03-01
A model for the nucleon as soliton of quarks interacting with classical meson fields is described. The theory, based on the linear sigma model, is renormalizable and capable of including sea quarks straightforwardly. Application to nuclear matter is made in a Wigner-Seitz approximation.
Sketch of J. R. Kantor's Psychological Interbehavioral Field Theory
ERIC Educational Resources Information Center
Delprato, Dennis J.; Smith, Noel W.
2009-01-01
We provide a sketch of J. R. Kantor's (1959, 1971) psychological interbehavioral field (IBF) theory by identifying 9 essential points and briefly discussing each. The main emphasis of this sketch is on the foundation of Kantor's thinking, the IBF. Suggestions for further study are provided.
The effective field theory of K-mouflage
Brax, Philippe; Valageas, Patrick E-mail: patrick.valageas@cea.fr
2016-01-01
We describe K-mouflage models of modified gravity using the effective field theory of dark energy. We show how the Lagrangian density K defining the K-mouflage models appears in the effective field theory framework, at both the exact fully nonlinear level and at the quadratic order of the effective action. We find that K-mouflage scenarios only generate the operator (δg{sup 00}{sub (u)}){sup n} at each order n. We also reverse engineer K-mouflage models by reconstructing the whole effective field theory, and the full cosmological behaviour, from two functions of the Jordan-frame scale factor in a tomographic manner. This parameterisation is directly related to the implementation of the K-mouflage screening mechanism: screening occurs when K' is large in a dense environment such as the deep matter and radiation eras. In this way, K-mouflage can be easily implemented as a calculable subclass of models described by the effective field theory of dark energy which could be probed by future surveys.
Morse theory for vector fields and the Witten Laplacian
Enciso, Alberto; Peralta-Salas, Daniel
2009-05-06
In this paper we informally review some recent developments on the analytical approach to Morse-type inequalities for vector fields. Throughout this work we focus on the main ideas of this approach and emphasize the application of the theory to concrete examples.
Quantum processes: A Whiteheadian interpretation of quantum field theory
NASA Astrophysics Data System (ADS)
Bain, Jonathan
Quantum processes: A Whiteheadian interpretation of quantum field theory is an ambitious and thought-provoking exercise in physics and metaphysics, combining an erudite study of the very complex metaphysics of A.N. Whitehead with a well-informed discussion of contemporary issues in the philosophy of algebraic quantum field theory. Hättich's overall goal is to construct an interpretation of quantum field theory. He does this by translating key concepts in Whitehead's metaphysics into the language of algebraic quantum field theory. In brief, this Hättich-Whitehead (H-W, hereafter) interpretation takes "actual occasions" as the fundamental ontological entities of quantum field theory. An actual occasion is the result of two types of processes: a "transition process" in which a set of initial possibly-possessed properties for the occasion (in the form of "eternal objects") is localized to a space-time region; and a "concrescence process" in which a subset of these initial possibly-possessed properties is selected and actualized to produce the occasion. Essential to these processes is the "underlying activity", which conditions the way in which properties are initially selected and subsequently actualized. In short, under the H-W interpretation of quantum field theory, an initial set of possibly-possessed eternal objects is represented by a Boolean sublattice of the lattice of projection operators determined by a von Neumann algebra R (O) associated with a region O of Minkowski space-time, and the underlying activity is represented by a state on R (O) obtained by conditionalizing off of the vacuum state. The details associated with the H-W interpretation involve imposing constraints on these representations motivated by principles found in Whitehead's metaphysics. These details are spelled out in the three sections of the book. The first section is a summary and critique of Whitehead's metaphysics, the second section introduces the formalism of algebraic quantum field
PyR@TE. Renormalization group equations for general gauge theories
NASA Astrophysics Data System (ADS)
Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.
2014-03-01
Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer
Field theory on R× S 3 topology: Lagrangian formulation
NASA Astrophysics Data System (ADS)
Carmeli, M.; Malka, A.
1990-01-01
A brief description of the ordinary field theory, from the variational and Noether's theorem point of view, is outlined. A discussion is then given of the field equations of Klein-Gordon, Schrödinger, Dirac, Weyl, and Maxwell in their ordinary form on the Minkowskian space-time manifold as well as on the topological space-time manifold R × S3 as they were formulated by Carmeli and Malin, including the latter's most general solutions. We then formulate the general variational principle in the R × S3 topological space, from which we derive the field equations in this space.
Finite temperature scalar field theory in the early universe
Leutwyler, H.; Mallik, S. )
1991-01-01
The authors study a scalar Higgs field in an expanding Robertson-Walker geometry, using the real time formulation of Semenoff and Weiss. It is shown that the density matrix associated with the Hamiltonian at a sharp time describes a state for which perturbation theory is not renormalizable and an alternative, renormalizable characterization of thermal equilibrium is given. They calculate the thermal quantum fluctuations surrounding a classical field and discuss the characteristic time scales occurring in the evolution of a scalar field from an initial radiation dominated phase of thermal equilibrium to an unstable, inflationary de Sitter phase.
Massive basketball diagram for a thermal scalar field theory
Andersen, Jens O.; Braaten, Eric; Strickland, Michael
2000-08-15
The ''basketball diagram'' is a three-loop vacuum diagram for a scalar field theory that cannot be expressed in terms of one-loop diagrams. We calculate this diagram for a massive scalar field at nonzero temperature, reducing it to expressions involving three-dimensional integrals that can be easily evaluated numerically. We use this result to calculate the free energy for a massive scalar field with a {phi}{sup 4} interaction to three-loop order. (c) 2000 The American Physical Society.
Overcoming Denial through the Group: A Test of Acceptance Theory.
ERIC Educational Resources Information Center
Rugel, Robert P.; Barry, Denise
1990-01-01
Found participants (N=28) in alcohol treatment groups showed decreases in denial of drinking problems and decreases in psychopathology following 12 weeks of group counseling. Determined greater self-acceptance was associated with experiencing acceptance by group and with greater decreases in denial; decreases in denial and psychopathology were…
When Group Membership Gets Personal: A Theory of Identity Fusion
ERIC Educational Resources Information Center
Swann, William B., Jr.; Jetten, Jolanda; Gomez, Angel; Whitehouse, Harvey; Bastian, Brock
2012-01-01
Identity fusion is a relatively unexplored form of alignment with groups that entails a visceral feeling of oneness with the group. This feeling is associated with unusually porous, highly permeable borders between the personal and social self. These porous borders encourage people to channel their personal agency into group behavior, raising the…
Morse Theory for Flows in Presence of a Symmetry Group.
1984-07-01
divided in six sections: The first two are introductory. In section I I recall the main definitions about to group actions on topological spaces and I...nl nm rl - - - . * .1.5 1. Group actions on topological spaces . Let X be a topological space and G a group with the multiplicative
Universal entanglement spectra of gapped one-dimensional field theories
NASA Astrophysics Data System (ADS)
Cho, Gil Young; Ludwig, Andreas W. W.; Ryu, Shinsei
2017-03-01
We discuss the entanglement spectrum of the ground state of a (1+1)-dimensional system in a gapped phase near a quantum phase transition. In particular, in proximity to a quantum phase transition described by a conformal field theory (CFT), the system is represented by a gapped Lorentz invariant field theory in the "scaling limit" (correlation length ξ much larger than microscopic "lattice" scale "a "), and can be thought of as a CFT perturbed by a relevant perturbation. We show that for such (1+1) gapped Lorentz invariant field theories in infinite space, the low-lying entanglement spectrum obtained by tracing out, say, left half-infinite space, is precisely equal to the physical spectrum of the unperturbed gapless, i.e., conformal field theory defined on a finite interval of length Lξ=ln(ξ /a ) with certain boundary conditions. In particular, the low-lying entanglement spectrum of the gapped theory is the finite-size spectrum of a boundary conformal field theory, and is always discrete and universal. Each relevant perturbation, and thus each gapped phase in proximity to the quantum phase transition, maps into a particular boundary condition. A similar property has been known to hold for Baxter's corner transfer matrices in a very special class of fine-tuned, namely, integrable off-critical lattice models, for the entire entanglement spectrum and independent of the scaling limit. In contrast, our result applies to completely general gapped Lorentz invariant theories in the scaling limit, without the requirement of integrability, for the low-lying entanglement spectrum. While the entanglement spectrum of the ground state of a gapped theory on a finite interval of length 2 R with suitable boundary conditions, bipartitioned into two equal pieces, turns out to exhibit a crossover between the finite-size spectra of the same CFT with in general different boundary conditions as the system size R crosses the correlation length from the "critical regime'' R ≪ξ to the
Topologically stratified energy minimizers in a product Abelian field theory
NASA Astrophysics Data System (ADS)
Han, Xiaosen; Yang, Yisong
2015-09-01
We study a recently developed product Abelian gauge field theory by Tong and Wong hosting magnetic impurities. We first obtain a necessary and sufficient condition for the existence of a unique solution realizing such impurities in the form of multiple vortices. We next reformulate the theory into an extended model that allows the coexistence of vortices and anti-vortices. The two Abelian gauge fields in the model induce two species of magnetic vortex-lines resulting from Ns vortices and Ps anti-vortices (s = 1, 2) realized as the zeros and poles of two complex-valued Higgs fields, respectively. An existence theorem is established for the governing equations over a compact Riemann surface S which states that a solution with prescribed N1, N2 vortices and P1, P2 anti-vortices of two designated species exists if and only if the inequalities
Quantum field theory for condensation of bosons and fermions
De Souza, Adriano N.; Filho, Victo S.
2013-03-25
In this brief review, we describe the formalism of the quantum field theory for the analysis of the condensation phenomenon in bosonic systems, by considering the cases widely verified in laboratory of trapped gases as condensate states, either with attractive or with repulsive two-body interactions. We review the mathematical formulation of the quantum field theory for many particles in the mean-field approximation, by adopting contact interaction potential. We also describe the phenomenon of condensation in the case of fermions or the degenerate Fermi gas, also verified in laboratory in the crossover BEC-BCS limit. We explain that such a phenomenon, equivalent to the bosonic condensation, can only occur if we consider the coupling of particles in pairs behaving like bosons, as occurs in the case of Cooper's pairs in superconductivity.
On the History of Unified Field Theories. Part II. (ca. 1930-ca. 1965)
NASA Astrophysics Data System (ADS)
Goenner, Hubert F. M.
2014-12-01
The present review intends to provide an overall picture of the research concerning classical unified field theory, worldwide, in the decades between the mid-1930 and mid-1960. Main themes are the conceptual and methodical development of the field, the interaction among the scientists working in it, their opinions and interpretations. Next to the most prominent players, A. Einstein and E. Schrödinger, V. Hlavatý and the French groups around A. Lichnerowicz, M.-A. Tonnelat, and Y. Thiry are presented. It is shown that they have given contributions of comparable importance. The review also includes a few sections on the fringes of the central topic like Born-Infeld electromagnetic theory or scalar-tensor theory. Some comments on the structure and organization of research-groups are also made.
Kriz, Igor; Loebl, Martin; Somberg, Petr
2013-05-15
We study various mathematical aspects of discrete models on graphs, specifically the Dimer and the Ising models. We focus on proving gluing formulas for individual summands of the partition function. We also obtain partial results regarding conjectured limits realized by fermions in rational conformal field theories.
Testing Belbin's Team Role Theory of Effective Groups.
ERIC Educational Resources Information Center
Prichard, Jane S.; Stanton, Neville A.
1999-01-01
Belbin's theory that teams with a wide range of roles are more effective than those with role imbalance was tested with six teams composed of individuals with homogenous roles and six with mixed roles. Mixed teams performed better on team tasks. (SK)
Tensor Networks for Lattice Gauge Theories with Continuous Groups
NASA Astrophysics Data System (ADS)
Tagliacozzo, L.; Celi, A.; Lewenstein, M.
2014-10-01
We discuss how to formulate lattice gauge theories in the tensor-network language. In this way, we obtain both a consistent-truncation scheme of the Kogut-Susskind lattice gauge theories and a tensor-network variational ansatz for gauge-invariant states that can be used in actual numerical computations. Our construction is also applied to the simplest realization of the quantum link models or gauge magnets and provides a clear way to understand their microscopic relation with the Kogut-Susskind lattice gauge theories. We also introduce a new set of gauge-invariant operators that modify continuously Rokhsar-Kivelson wave functions and can be used to extend the phase diagrams of known models. As an example, we characterize the transition between the deconfined phase of the Z2 lattice gauge theory and the Rokhsar-Kivelson point of the U (1 ) gauge magnet in 2D in terms of entanglement entropy. The topological entropy serves as an order parameter for the transition but not the Schmidt gap.
Theories in Developing Oral Communication for Specific Learner Group
ERIC Educational Resources Information Center
Hadi, Marham Jupri
2016-01-01
The current article presents some key theories most relevant to the development of oral communication skills in an Indonesian senior high school. Critical analysis on the learners' background is employed to figure out their strengths and weaknesses. The brief overview of the learning context and learners' characteristic are used to identify which…
Positive energy conditions in 4D conformal field theory
NASA Astrophysics Data System (ADS)
Farnsworth, Kara; Luty, Markus A.; Prilepina, Valentina
2016-10-01
We argue that all consistent 4D quantum field theories obey a spacetime-averaged weak energy inequality < T 00> ≥ - C/L 4, where L is the size of the smearing region, and C is a positive constant that depends on the theory. If this condition is violated, the theory has states that are indistinguishable from states of negative total energy by any local measurement, and we expect instabilities or other inconsistencies. We apply this condition to 4D conformal field theories, and find that it places constraints on the OPE coefficients of the theory. The constraints we find are weaker than the "conformal collider" constraints of Hofman and Maldacena. In 3D CFTs, the only constraint we find is equivalent to the positivity of 2-point function of the energy-momentum tensor, which follows from unitarity. Our calculations are performed using momentum-space Wightman functions, which are remarkably simple functions of momenta, and may be of interest in their own right.
Double metric, generalized metric, and α' -deformed double field theory
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Zwiebach, Barton
2016-03-01
We relate the unconstrained "double metric" of the "α' -geometry" formulation of double field theory to the constrained generalized metric encoding the spacetime metric and b -field. This is achieved by integrating out auxiliary field components of the double metric in an iterative procedure that induces an infinite number of higher-derivative corrections. As an application, we prove that, to first order in α' and to all orders in fields, the deformed gauge transformations are Green-Schwarz-deformed diffeomorphisms. We also prove that to first order in α' the spacetime action encodes precisely the Green-Schwarz deformation with Chern-Simons forms based on the torsionless gravitational connection. This seems to be in tension with suggestions in the literature that T-duality requires a torsionful connection, but we explain that these assertions are ambiguous since actions that use different connections are related by field redefinitions.
Axiomatics of Galileo-invariant quantum field theory
Dadashev, L.A.
1986-03-01
The aim of this paper is to construct the axiomatics of Galileo-invariant quantum field theory. The importance of this problem is demonstrated from various points of view: general properties that the fields and observables must satisfy are considered; S-matrix nontriviality of one such model is proved; and the differences from the relativistic case are discussed. The proposed system of axioms is in many respects analogous to Wightman axiomatics, but is less general. The main result is contained in theorems which describe the admissible set of initial fields and total Hamiltonians, i.e., precisely the two entities that completely determine interacting fields. The author considers fields that prove the independence of some axioms.
A tracer-kinetic field theory for medical imaging.
Sourbron, Steven
2014-04-01
Dynamic imaging data are currently analyzed with a tracer-kinetic theory developed for individual time curves measured over whole organs. The assumption is that voxels represent isolated systems which all receive indicator through the same arterial inlet. This leads to well-known systematic errors, but also fails to exploit the spatial structure of the data. In this study, a more general theoretical framework is developed which makes full use of the specific structure of image data. The theory encodes the fact that voxels receive indicator from their immediate neighbors rather than from an upstream arterial input. This results in a tracer-kinetic field theory where the tissue parameters are functions of space which can be measured by analyzing the temporal and spatial patterns in the concentrations. The implications are evaluated through a number of field models for common tissue types. The key benefits of a tracer-kinetic field theory are that: 1) long-standing systematic errors can be corrected, specifically the issue of bolus dispersion and the contamination of large-vessel blood flow on tissue perfusion measurements; 2) additional tissue parameters can be measured that characterize convective or diffusive exchange between voxels; 3) the need to measure a separate arterial input function can be eliminated.
Towards Noncommutative Topological Quantum Field Theory: New invariants for 3-manifolds
NASA Astrophysics Data System (ADS)
Zois, I. P.
2016-08-01
We present some ideas for a possible Noncommutative Topological Quantum Field Theory (NCTQFT for short) and Noncommutative Floer Homology (NCFH for short). Our motivation is two-fold and it comes both from physics and mathematics: On the one hand we argue that NCTQFT is the correct mathematical framework for a quantum field theory of all known interactions in nature (including gravity). On the other hand we hope that a possible NCFH will apply to practically every 3-manifold (and not only to homology 3-spheres as ordinary Floer Homology currently does). The two motivations are closely related since, at least in the commutative case, Floer Homology Groups constitute the space of quantum observables of (3+1)-dim Topological Quantum Field Theory. Towards this goal we define some new invariants for 3-manifolds using the space of taut codim-1 foliations modulo coarse isotopy along with various techniques from noncommutative geometry.
Heavy dark matter annihilation from effective field theory.
Ovanesyan, Grigory; Slatyer, Tracy R; Stewart, Iain W
2015-05-29
We formulate an effective field theory description for SU(2)_{L} triplet fermionic dark matter by combining nonrelativistic dark matter with gauge bosons in the soft-collinear effective theory. For a given dark matter mass, the annihilation cross section to line photons is obtained with 5% precision by simultaneously including Sommerfeld enhancement and the resummation of electroweak Sudakov logarithms at next-to-leading logarithmic order. Using these results, we present more accurate and precise predictions for the gamma-ray line signal from annihilation, updating both existing constraints and the reach of future experiments.
Dynamics of Compact Binaries in Effective Field Theory Formalism
NASA Astrophysics Data System (ADS)
Perrodin, Delphine
2010-02-01
Coalescing compact binaries are predicted to be powerful emitters of gravitational waves, and provide a strong gravity environment ideal for the testing of gravity theories. We study the gravitational dynamics in the early inspiral phase of coalescing compact binaries using Non-Relativistic General Relativity (NRGR) - an effective field theory formalism based on the Post-Newtonian approximation to General Relativity, but which provides a consistent lagrangian framework and a systematic way in which to study binary dynamics and gravitational wave emission. We calculate in this framework the spin-orbit correction to the newtonian potential at 2.5 PN. )
Lagrangian-Hamiltonian unified formalism for field theory
NASA Astrophysics Data System (ADS)
Echeverría-Enríquez, Arturo; López, Carlos; Marín-Solano, Jesús; Muñoz-Lecanda, Miguel C.; Román-Roy, Narciso
2004-01-01
The Rusk-Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this description comprises the main features of the Lagrangian and Hamiltonian formalisms, both for the regular and singular cases. This formulation is a first step toward further applications in optimal control theory for partial differential equations.
Nuclear axial currents in chiral effective field theory
Baroni, Alessandro; Girlanda, Luca; Pastore, Saori; ...
2016-01-11
Two-nucleon axial charge and current operators are derived in chiral effective field theory up to one loop. The derivation is based on time-ordered perturbation theory and accounts for cancellations between the contributions of irreducible diagrams and the contributions owing to nonstatic corrections from energy denominators of reducible diagrams. Ultraviolet divergencies associated with the loop corrections are isolated in dimensional regularization. The resulting axial current is finite and conserved in the chiral limit, while the axial charge requires renormalization. As a result, a complete set of contact terms for the axial charge up to the relevant order in the power countingmore » is constructed.« less
Nuclear axial currents in chiral effective field theory
Baroni, Alessandro; Girlanda, Luca; Pastore, Saori; Schiavilla, Rocco; Viviani, Michele
2016-01-11
Two-nucleon axial charge and current operators are derived in chiral effective field theory up to one loop. The derivation is based on time-ordered perturbation theory and accounts for cancellations between the contributions of irreducible diagrams and the contributions owing to nonstatic corrections from energy denominators of reducible diagrams. Ultraviolet divergencies associated with the loop corrections are isolated in dimensional regularization. The resulting axial current is finite and conserved in the chiral limit, while the axial charge requires renormalization. As a result, a complete set of contact terms for the axial charge up to the relevant order in the power counting is constructed.
Nucleon propagation through nuclear matter in chiral effective field theory
NASA Astrophysics Data System (ADS)
Mallik, S.; Mishra, H.
2007-05-01
We treat the propagation of a nucleon in nuclear matter by evaluating the ensemble average of the two-point function of the nucleon currents in the framework of chiral effective field theory. We first derive the effective parameters of the nucleon to one loop. The resulting formula for the effective mass has been known since before and gives an absurd value at normal nuclear density. We then modify it following Weinberg’s method for the two-nucleon system in the effective theory. Our results for the effective mass and the width of the nucleon are compared with those in the literature.
Effective field theory for dilute fermions with pairing
Furnstahl, R.J. Hammer, H.-W. Puglia, S.J.
2007-11-15
Effective field theory (EFT) methods for a uniform system of fermions with short-range, natural interactions are extended to include pairing correlations, as part of a program to develop a systematic Kohn-Sham density functional theory (DFT) for medium and heavy nuclei. An effective action formalism for local composite operators leads to a free-energy functional that includes pairing by applying an inversion method order by order in the EFT expansion. A consistent renormalization scheme is demonstrated for the uniform system through next-to-leading order, which includes induced-interaction corrections to pairing.
The principle of stationary variance in quantum field theory
NASA Astrophysics Data System (ADS)
Siringo, Fabio
2014-02-01
The principle of stationary variance is advocated as a viable variational approach to quantum field theory (QFT). The method is based on the principle that the variance of energy should be at its minimum when the state of a quantum system reaches its best approximation for an eigenstate. While not too much popular in quantum mechanics (QM), the method is shown to be valuable in QFT and three special examples are given in very different areas ranging from Heisenberg model of antiferromagnetism (AF) to quantum electrodynamics (QED) and gauge theories.
Advanced mean-field theory of the restricted Boltzmann machine
NASA Astrophysics Data System (ADS)
Huang, Haiping; Toyoizumi, Taro
2015-05-01
Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean-field theory based on the Bethe approximation. Our theory provides an efficient message-passing-based method that evaluates not only the partition function (free energy) but also its gradients without requiring statistical sampling. The results are compared with those obtained by the computationally expensive sampling-based method.
Large N correlation functions in superconformal field theories
NASA Astrophysics Data System (ADS)
Rodriguez-Gomez, Diego; Russo, Jorge G.
2016-06-01
We compute correlation functions of chiral primary operators in mathcal{N}=2 super-conformal theories at large N using a construction based on supersymmetric localization recently developed by Gerchkovitz et al. We focus on mathcal{N}=4 SYM as well as on supercon-formal QCD. In the case of mathcal{N}=4 we recover the free field theory results as expected due to non-renormalization theorems. In the case of superconformal QCD we study the planar expansion in the large N limit. The final correlators admit a simple generalization to a finite N formula which exactly matches the various small N results in the literature.
Einstein-aether theory with a Maxwell field: General formalism
Balakin, Alexander B.; Lemos, José P.S.
2014-11-15
We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.
Thermal field theory applications in modern aspects of high energy physics
NASA Astrophysics Data System (ADS)
Pastras, Georgios
In the first part, We find non-supersymmetric metastable vacua in four dimensional N = 2 gauge theories softly broken to N = 1 by a superpotential term. First we study the SU(2) gauge theory without flavors. We find the spectrum and lifetime of the metastable vacuum and possible embeddings of the model in UV complete theories. Then we consider larger gauge group theories with flavors. Finally we study the SU(2) theory without flavors at high temperatures and we demonstrate that the cooling universe can settle in the metastable vacuum, provided that: first the superpotential term is not arbitrarily small in comparison to the strong coupling scale of the gauge theory, and second the metastable vacuum lies in the strongly coupled region of the moduli space. In the second part, the local and global thermal phase structure for asymptotically AdS black holes charged under a U(1) group, with both Gauss-Bonnet and quartic field strength corrections, is mapped out for all parameter space. The analysis is performed in the grand canonical ensemble and at an arbitrary number of dimensions. New metastable configurations are exhibited both for the pure Gauss-Bonnet theory as well as the pure higher derivative gauge theory and combinations thereof. Finally, a secondary Hawking-Page transition between the smaller black hole and thermal AdS space is observed when both corrections are turned on.
Chaos and order in non-integrable model field theories
Campbell, D.K.; Peyrard, M.
1989-01-01
We illustrate the presence of chaos and order in non-integrable, classical field theories, which we view as many-degree-of-freedom Hamiltonian nonlinear dynamical systems. For definiteness, we focus on the {chi}{sup 4} theory and compare and contrast it with the celebrated integrable sine-Gordon equation. We introduce and investigate two specific problems: the interactions of solitary kink''-like waves in non-integrable theories; and the existence of stable breather'' solutions -- spatially-localized, time-periodic nonlinear waves -- in the {chi}{sup 4} theory. For the former problem we review the rather well developed understanding, based on a combination of computational simulations and heuristic analytic models, of the presence of a sequence of resonances in the kink-antikink interactions as a function of the relative velocity of the interaction. For the latter problem we discuss first the case of the continuum {chi}{sup 4} theory. We discuss the multiple-scale asymptotic perturbation theory arguments which first suggested the existence of {chi}{sup 4} breathers, then the subsequent discovery of terms beyond-all-orders'' in the perturbation expansion which destroy the putative breather, and finally, the recent rigorous proofs of the non-existence of breathers in the continuum theory. We then present some very recent numerical results on the existence of breathers in discrete {chi}{sup 4} theories which show an intricate interweaving of stable and unstable breather solutions on finite discrete lattices. We develop a heuristic theoretical explanation of the regions of stability and instability.
A theory of leadership in human cooperative groups.
Hooper, Paul L; Kaplan, Hillard S; Boone, James L
2010-08-21
Two types of models aim to account the origins of rank differentiation and social hierarchy in human societies. Conflict models suggest that the formation of social hierarchies is synonymous with the establishment of relationships of coercive social dominance and exploitation. Voluntary or 'integrative' models, on the other hand, suggest that rank differentiation--the differentiation of leader from follower, ruler from ruled, or state from subject--may sometimes be preferred over more egalitarian social arrangements as a solution to the challenges of life in social groups, such as conflict over resources, coordination failures, and free-riding in cooperative relationships. Little formal theoretical work, however, has established whether and under what conditions individuals would indeed prefer the establishment of more hierarchical relationships over more egalitarian alternatives. This paper provides an evolutionary game theoretical model for the acceptance of leadership in cooperative groups. We propose that the effort of a leader can reduce the likelihood that cooperation fails due to free-riding or coordination errors, and that under some circumstances, individuals would prefer to cooperate in a group under the supervision of a leader who receives a share of the group's productivity than to work in an unsupervised group. We suggest, in particular, that this becomes an optimal solution for individual decision makers when the number of group members required for collective action exceeds the maximum group size at which leaderless cooperation is viable.
Studies on Quantum Field Theory and Statistical Mechanics
NASA Astrophysics Data System (ADS)
Zhang, Shoucheng
This dissertation is a summary of research in various areas of theoretical physics and is divided into three parts. In the first part, quantum fluctuations of the recently proposed superconducting cosmic strings are studied. It is found that vortices on the string world sheet represent an important class of fluctuation modes which tend to disorder the system. Both heuristic arguments and detailed renormalization group analysis reveal that these vortices do not appear in bound pairs but rather form a gas of free vortices. Based on this observation we argue that this fluctuation mode violates the topological conservation law on which superconductivity is based. Anomalies and topological aspects of supersymmetric quantum field theories are studied in the second part of this dissertation. Using the superspace formulation of the N = 1 spinning string, we obtain a path integral measure which is free from the world-sheet general coordinate as well as the supersymmetry anomalies and therefore determine the conformal anomaly and critical dimension of the spinning string. We also apply Fujikawa's formalism to computer the chiral anomaly in conformal as well as ordinary supergravity. Finally, we given a Noether-method construction of the supersymmetrized Chern-Simons term in five dimensional supergravity. In the last part of this dissertation, the soliton excitations in the quarter-filled Peierls-Hubbard model are investigated in both the large and the small U limit. For a strictly one dimensional system at zero temperature, we find that solitons in both limits are in one-to-one correspondence, while in the presence of weak three dimensional couplings or at finite temperature, the large U systems differ qualitatively from the small U systems in that the spin associated with the solitons ceases to be a sharp quantum observable.